Method of simulating indoor behavior of pesticidal compound

ABSTRACT

The present invention relates to a method of simulating an indoor behavior of a pesticidal compound, and aims to provide a simulation method which can process simultaneous differential equations necessary for simulation accurately in a short time, and to evaluate safety of the compound with respect to a human body. The simulation method includes a step of dividing an indoor environment into predetermined media and forming a differential equation concerning a fugacity of the compound in each of the media; a step of determining the fugacity of the compound in each of the media from the differential equation; a step of determining the indoor behavior of the compound from the fugacity of the compound in each of the media; a step of changing, in response to a fluctuation in mass balance of the compound indoors, a minute time unit used when solving the differential equation; and a step of evaluating, according to the indoor behavior of the compound, safety of the compound with respect to the human body.

TECHNICAL FIELD

The present invention relates to a method of simulating, when a chemicalcontaining a pesticidal compound is used indoors, an indoor behavior ofthe pesticidal compound including an estimation method of estimating theindoor behavior of the compound and a safety evaluating method ofevaluating its safety in human bodies by using the estimation method;and, in particular, to a method of simulating an indoor behavior of apesticidal compound in the case where a chemical containing thepesticidal compound is residually sprayed, sprayed in an indoor space,heated to vaporize, or sprayed over the whole floor area.

BACKGROUND ART

Conventionally known is a fugaciousness (hereinafter referred to asFugacity) model for simulating a behavior of a chemical material inglobal environment. The above-mentioned fugacity model utilizes Fugacitywhose unit is an external force by which the chemical material escapesfrom one medium to another medium, i.e., pressure. For example, when thechemical material concentration differs between two media A and B,concentrations in the respective media are expressed by:

 N _(A) /V _(A) =f _(A) Z _(A)

N _(B) /V _(B) =f _(B) Z _(B)

wherein N is chemical mass, V is volume of medium, f is Fugacity, and Zis Fugacity capacity of medium.

Here, while the mass N changes over time according to transference anddegradation of the chemical material between the media A and B; assumingthat volume V and Fugacity capacity Z are constant, the above-mentionedtwo expressions are represented as:

(df _(A) /dt)V _(A) Z _(A) =dN _(A)/dt=−(Degradation)_(A)±(Transference)_(AB)

(df _(B) /dt)V _(B) Z _(B) =dN _(B)/dt=−(Degradation)_(B)±(Transference)_(AB)

When Degradation and Transference in these two differential equationsare given, unknown parameters f_(A) and f_(B) can be determined bycalculation. When these parameters are respectively multiplied byFugacity capacity Z_(A) and Z_(B), the chemical material concentrationsin the respective media in a specific period of time can be simulated.

As an apparatus for simulating a behavior of a chemical material,Japanese Patent Application Laid-Open No. 64-88811 discloses aconfiguration of closed-space simulator which can perform simulation inresponse to any capacity of closed space without actually constructing aclosed space when evaluating temperature change of a specific gascomponent such as carbonic acid gas.

As a configuration for evaluating influence of a harmful material onhuman bodies, Japanese Patent Application Laid-Open No. 3-89146discloses a configuration of percutaneous absorption evaluationapparatus employing a vertical type diffusion cell which is a systemcloser to a clinical state than is a parallel type cell, thereby beingcapable of simultaneously measuring, in real time, the process of achemical being emitted from its base on the skin by optoacousticmeasurement and the process of the chemical infiltrating through theskin by absorptiometry.

Also, Japanese Patent Application Laid-Open No. 7-218496 discloses aconfiguration of system which uses the fact that a dissolution parameterinherently existing in a chemical material and a logarithmic value ofmedian lethal dose of the chemical material with respect to a mammal arein a specific correlation, estimating acute toxicity of the chemicalmaterial with respect to the mammal.

Further, simulations of indoor behavior of a pesticidal compound wheninsecticides are sprayed in an indoor space, electrically heated tovaporize in a room, and sprayed over the whole floor surface arerespectively disclosed in Y. Matoba et al., “A SIMULATION OFINSECTICIDES IN INDOOR AEROSOL SPACE SPRAYING,” Chemosphere, Vol.26,No.6, pp. 1167-1186, 1993; Y. Matoba et al., “INDOOR SIMULATION OFINSECTICIDES SUPPLIED WITH AN ELECTRIC VAPORIZER BY THE FUGACITY MODEL,”Chemosphere, Vol.28, No.4, pp.767-786, 1994; and Y. Matoba et al.,“INDOOR SIMULATION OF INSECTICIDES IN BROADCAST SPRAYING,” Chemosphere,Vol.30, No.2, pp. 345-365, 1995.

DISCLOSURE OF INVENTION

The above-mentioned simulation models, however, do not mention how tosolve differential equations, and minute time units set when solving thedifferential equations are assumed to be constant. Theoretically, thesmaller is the minute time unit, the longer becomes the calculationtime; whereas the solution would not converge when the minute time unitis large. Accordingly, in the case where a differential equationcontaining a parameter which changes over time is to be solved, when theminute time unit is set to a constant value so that the solution doesnot diverge, there is a problem that the processing speed of a computermust be enhanced.

Also, the above-mentioned simulation models fail to mention any securitywith respect to human bodies.

In order to solve the above-mentioned conventional problems, it is anobject of the present invention to provide a method of simulating anindoor behavior of a pesticidal compound, which can process simultaneousdifferential equations accurately in a short time by automaticallysetting a minute time unit.

In order to achieve the above-mentioned object, the method of simulatingan indoor behavior of a pesticidal compound in accordance with thepresent invention comprises a step of dividing an indoor environmentinto predetermined media (constituents) and forming a differentialequation concerning a fugacity of the compound in each of the media; astep of determining the fugacity of the compound in each of the mediafrom the differential equation; a step of determining the indoorbehavior of the compound from the fugacity of the compound in each ofthe media; and a step of changing, in response to a fluctuation in massbalance of the compound indoors, a minute time unit used when solvingthe differential equation.

As the indoor environment is divided into predetermined media, andexchanges of the chemical compound between the media and the like aretaken into account, simulation results close to the actual behavior ofthe compound can be obtained, while the minute time unit can be setautomatically in response to fluctuation in mass balance when solvingsimultaneous differential equations including a parameter which changesover time. Accordingly, when a computer processes the above-mentioneddifferential equation, accurate solutions can be obtained in a shorttime.

Preferably, the method of simulating an indoor behavior of a pesticidalcompound in accordance with the present invention further comprises astep of evaluating safety of the compound with respect to a human bodyaccording to the indoor behavior of the compound.

As a consequence of this configuration, the safety of the pesticidalcompound with respect to the human body can be evaluated accurately in ashort time. Accordingly, when formulating a chemical such as insecticideincluding the above-mentioned compound, simulation can be easilyrepeated while changing conditions, thereby making it easier toformulate a chemical having a high safety conforming to the aimedobject.

Further, the method of simulating an indoor behavior of a pesticidalcompound in accordance with the present invention may be such that theabove-mentioned compound is introduced into an indoor space as asolution containing the compound is residually sprayed; whereas theabove-mentioned media are a spraying site, suspended particles which aredivided into at least one kind according to size, indoor air, a floor, awall, and a ceiling.

Preferably, in this case, the differential equation at the spraying siteis a differential equation stating a relationship among temporal changeof fugacity of the compound at the spraying site, temporal change involume of the spraying site, amount of attachment of the suspendedparticles to the spraying site, amount of transference of the compoundbetween the spraying site and another medium, and change in amount ofdegradation of the compound at the spraying site; the differentialequation in the suspended particles is a differential equation stating arelationship among temporal change of fugacity of the compound in thesuspended particles, temporal change in volume of the suspendedparticles, amount of transference of the compound between the suspendedparticles and another medium, and change in amount of degradation of thecompound in the suspended particles; the differential equation in theindoor air is a differential equation stating a relationship amongtemporal change of fugacity of the compound in the indoor air, amount ofdischarge of the compound outdoors, amount of transference of thecompound between the indoor air and another medium, and change in amountof degradation of the compound in the indoor air; the differentialequation at the floor is a differential equation stating a relationshipamong temporal change of fugacity of the compound at the floor, temporalchange in volume of the floor, amount of attachment of the suspendedparticles to the floor, amount of transference of the compound betweenthe floor and another medium, and change in amount of degradation of thecompound at the floor; the differential equation at the wall is adifferential equation stating a relationship among temporal change offugacity of the compound at the wall, temporal change in volume of thewall, amount of attachment of the suspended particles to the wall,amount of transference of the compound between the wall and anothermedium, and change in amount of degradation of the compound at the wall;and the differential equation at the ceiling is a differential equationstating a relationship among temporal change of fugacity of the compoundat the ceiling, temporal change in volume of the ceiling, amount ofattachment of the suspended particles to the ceiling, amount oftransference of the compound between the ceiling and another medium, andchange in amount of degradation of the compound at the ceiling.

The method of simulating an indoor behavior of a pesticidal compound inaccordance with the present invention may be such that theabove-mentioned compound is introduced into an indoor space as asolution containing the compound is spatially sprayed; whereas theabove-mentioned media are suspended particles which are divided into atleast one kind according to size, indoor air, a floor, a wall, and aceiling.

Preferably, in this case, the differential equation in the suspendedparticles is a differential equation stating a relationship amongtemporal change of fugacity of the compound in the suspended particles,temporal change in volume of the suspended particles, amount oftransference of the compound between the suspended particles and anothermedium, and change in amount of degradation of the compound in thesuspended particles; the differential equation in the indoor air is adifferential equation stating a relationship among temporal change offugacity of the compound in the indoor air, amount of discharge of thecompound outdoors, amount of transference of the compound between theindoor air and another medium, and change in amount of degradation ofthe compound in the indoor air; the differential equation at the flooris a differential equation stating a relationship among temporal changeof fugacity of the compound at the floor, temporal change in volume ofthe floor, amount of attachment of the suspended particles to the floor,amount of transference of the compound between the floor and anothermedium, and change in amount of degradation of the compound at thefloor; the differential equation at the wall is a differential equationstating a relationship among temporal change of fugacity of the compoundat the wall, temporal change in volume of the wall, amount of attachmentof the suspended particles to the wall, amount of transference of thecompound between the wall and another medium, and change in amount ofdegradation of the compound at the wall; and the differential equationat the ceiling is a differential equation stating a relationship amongtemporal change of fugacity of the compound at the ceiling, temporalchange in volume of the ceiling, amount of attachment of the suspendedparticles to the ceiling, amount of transference of the compound betweenthe ceiling and another medium, and change in amount of degradation ofthe compound at the ceiling.

The method of simulating an indoor behavior of a pesticidal compound inaccordance with the present invention may be such that theabove-mentioned compound is introduced into an indoor space as asolution containing the compound is heated to vaporize; whereas theabove-mentioned media are condensed particles which are divided into atleast one kind according to generation and extinction,high-concentration air, medium-concentration air, low-concentration air,a floor, a wall, and a ceiling which is divided into at least one kindaccording to compound concentration.

Preferably, in this case, the differential equation in the condensedparticles is a differential equation stating a relationship amongtemporal change of fugacity of the compound in the condensed particles,temporal change in volume of the condensed particles, amount oftransference of the compound between the condensed particles and anothermedium, and change in amount of degradation of the compound in thecondensed particles; the differential equation in the high-concentrationair is a differential equation stating a relationship among temporalchange of fugacity of the compound in the high-concentration air, amountof discharge of the compound, amount of transference of the compoundbetween the high-concentration air and another medium, and change inamount of degradation of the compound in the high-concentration air; thedifferential equation in the medium-concentration air is a differentialequation stating a relationship among temporal change of fugacity of thecompound in the medium-concentration air, amount of transference of thecompound between the medium-concentration air and another medium, andchange in amount of degradation of the compound in themedium-concentration air; the differential equation in thelow-concentration air is a differential equation stating a relationshipamong temporal change of fugacity of the compound in thelow-concentration air, amount of discharge of the compound outdoors,amount of transference of the compound between the low-concentration airand another medium, and change in amount of degradation of the compoundin the low-concentration air; the differential equation at the floor isa differential equation stating a relationship among temporal change offugacity of the compound at the floor, temporal change in volume of thefloor, amount of transference of the compound between the floor andanother medium, and change in amount of degradation of the compound atthe floor; the differential equation at the wall is a differentialequation stating a relationship among temporal change of fugacity of thecompound at the wall, temporal change in volume of the wall, amount oftransference of the compound between the wall and another medium, andchange in amount of degradation of the compound at the wall; and thedifferential equation at the ceiling is a differential equation statinga relationship among temporal change of fugacity of the compound at theceiling, temporal change in volume of the ceiling, amount oftransference of the compound between the ceiling and another medium, andchange in amount of degradation of the compound at the ceiling.

The method of simulating an indoor behavior of a pesticidal compound inaccordance with the present invention may be such that theabove-mentioned compound is introduced into an indoor space as asolution containing the compound is sprayed over the whole floor;whereas the above-mentioned media are suspended particles which aredivided into at least one kind according to size, indoor air, a floor, awall, and a ceiling.

Preferably, in this case, the differential equation in the suspendedparticles is a differential equation stating a relationship amongtemporal change of fugacity of the compound in the suspended particles,temporal change in volume of the suspended particles, amount oftransference of the compound between the suspended particles and anothermedium, and change in amount of degradation of the compound in thesuspended particles; the differential equation in the indoor air is adifferential equation stating a relationship among temporal change offugacity of the compound in the indoor air, amount of discharge of thecompound outdoors, amount of transference of the compound between theindoor air and another medium, and change in amount of degradation ofthe compound in the indoor air; the differential equation at the flooris a differential equation stating a relationship among temporal changeof fugacity of the compound at the floor, temporal change in volume ofthe floor, amount of attachment of the suspended particles to the floor,amount of transference of the compound between the floor and anothermedium, and change in amount of degradation of the compound at thefloor; the differential equation at the wall is a differential equationstating a relationship among temporal change of fugacity of the compoundat the wall, temporal change in volume of the wall, amount of attachmentof the suspended particles to the wall, amount of transference of thecompound between the wall and another medium, and change in amount ofdegradation of the compound at the wall; and the differential equationat the ceiling is a differential equation stating a relationship amongtemporal change of fugacity of the compound at the ceiling, temporalchange in volume of the ceiling, amount of attachment of the suspendedparticles to the ceiling, amount of transference of the compound betweenthe ceiling and another medium, and change in amount of degradation ofthe compound at the ceiling.

The method of simulating an indoor behavior of a pesticidal compound inaccordance with the present invention may be such that the floor isconstituted by a rug having ears of fiber, whereas a space between theears is added to the above-mentioned media.

Preferably, in this case, the differential equation in the space betweenthe ears is a differential equation stating a relationship amongtemporal change of fugacity of the compound in the space between theears, temporal change in volume of the solution containing the compoundin the space between the ears, amount of attachment of the compound intothe space portion between the ears by falling, amount of transference ofthe compound between the space portion between the ears and anothermedium, and change in amount of degradation of the compound in the spaceportion between the ears.

Even in the case where a rug having ears of fiber is spread on thefloor, when the space between the ears is further added to the media,the behavior of the compound can be simulated accurately, thus allowingvarious kinds of simulations to be performed.

In order to achieve the above-mentioned object, the computer programproduct of the present invention is a computer program product to beused together with an information processing apparatus comprising inputmeans for receiving a data input from outside, display means, andreadout means for reading out information from a computer-usable storagemedium; the computer program product comprising a computer-usablestorage medium which has a program area for storing a program and has acomputer-readable program materialized in the storage medium forcausing, according to data input from the input means, the display meansto display a result of simulation of an indoor behavior of a pesticidalcompound; the computer program product comprising, in the program area,a program for dividing an indoor environment into predetermined mediaand forming a differential equation concerning a fugacity of thecompound, a program for determining the fugacity of the compound in eachof the media from the differential equation; a program for determiningthe indoor behavior of the compound from the fugacity of the compound ineach of the media, and a program for changing, in response to afluctuation in mass balance of the compound indoors, a minute time unitused when solving the differential equation.

As the indoor environment is divided into predetermined media, andexchanges of the chemical compound between the media and the like aretaken into account, simulation results close to the actual behavior ofthe compound can be obtained, while the minute time unit can be setautomatically in response to fluctuation in mass balance when solvingsimultaneous differential equations including a parameter which changesover time. Accordingly, when a computer processes the above-mentioneddifferential equation, accurate solutions can be obtained in a shorttime.

Preferably, the computer program product further comprises, in theprogram area, a program for evaluating safety of the compound withrespect to a human body according to the indoor behavior of thecompound.

As a consequence of this configuration, the safety of the pesticidalcompound with respect to the human body can be evaluated accurately in ashort time. Accordingly, when formulating a chemical such as insecticideincluding the above-mentioned compound, simulation can be easilyrepeated while changing conditions, thereby making it easier toformulate a chemical having a high safety conforming to the aimedobject.

The computer program product of the present invention may be such thatthe above-mentioned compound is introduced into an indoor space as asolution containing the compound is residually sprayed; whereas theabove-mentioned media are a spraying site, suspended particles which aredivided into at least one kind according to size, indoor air, a floor, awall, and a ceiling.

Preferably, in this case, the differential equation at the spraying siteis a differential equation stating a relationship among temporal changeof fugacity of the compound at the spraying site, temporal change involume of the spraying site, amount of attachment of the suspendedparticles to the spraying site, amount of transference of the compoundbetween the spraying site and another medium, and change in amount ofdegradation of the compound at the spraying site; the differentialequation in the suspended particles is a differential equation stating arelationship among temporal change of fugacity of the compound in thesuspended particles, temporal change in volume of the suspendedparticles, amount of transference of the compound between the suspendedparticles and another medium, and change in amount of degradation of thecompound in the suspended particles; the differential equation in theindoor air is a differential equation stating a relationship amongtemporal change of fugacity of the compound in the indoor air, amount ofdischarge of the compound outdoors, amount of transference of thecompound between the indoor air and another medium, and change in amountof degradation of the compound in the indoor air; the differentialequation at the floor is a differential equation stating a relationshipamong temporal change of fugacity of the compound at the floor, temporalchange in volume of the floor, amount of attachment of the suspendedparticles to the floor, amount of transference of the compound betweenthe floor and another medium, and change in amount of degradation of thecompound at the floor; the differential equation at the wall is adifferential equation stating a relationship among temporal change offugacity of the compound at the wall, temporal change in volume of thewall, amount of attachment of the suspended particles to the wall,amount of transference of the compound between the wall and anothermedium, and change in amount of degradation of the compound at the wall;and the differential equation at the ceiling is a differential equationstating a relationship among temporal change of fugacity of the compoundat the ceiling, temporal change in volume of the ceiling, amount ofattachment of the suspended particles to the ceiling, amount oftransference of the compound between the ceiling and another medium, andchange in amount of degradation of the compound at the ceiling.

The computer program product of the present invention may be such thatthe above-mentioned compound is introduced into an indoor space as asolution containing the compound is spatially sprayed; whereas theabove-mentioned media are suspended particles which are divided into atleast one kind according to size, indoor air, a floor, a wall, and aceiling.

Preferably, in this case, the differential equation in the suspendedparticles is a differential equation stating a relationship amongtemporal change of fugacity of the compound in the suspended particles,temporal change in volume of the suspended particles, amount oftransference of the compound between the suspended particles and anothermedium, and change in amount of degradation of the compound in thesuspended particles; the differential equation in the indoor air is adifferential equation stating a relationship among temporal change offugacity of the compound in the indoor air, amount of discharge of thecompound outdoors, amount of transference of the compound between theindoor air and another medium, and change in amount of degradation ofthe compound in the indoor air; the differential equation at the flooris a differential equation stating a relationship among temporal changeof fugacity of the compound at the floor, temporal change in volume ofthe floor, amount of attachment of the suspended particles to the floor,amount of transference of the compound between the floor and anothermedium, and change in amount of degradation of the compound at thefloor; the differential equation at the wall is a differential equationstating a relationship among temporal change of fugacity of the compoundat the wall, temporal change in volume of the wall, amount of attachmentof the suspended particles to the wall, amount of transference of thecompound between the wall and another medium, and change in amount ofdegradation of the compound at the wall; and the differential equationat the ceiling is a differential equation stating a relationship amongtemporal change of fugacity of the compound at the ceiling, temporalchange in volume of the ceiling, amount of attachment of the suspendedparticles to the ceiling, amount of transference of the compound betweenthe ceiling and another medium, and change in amount of degradation ofthe compound at the ceiling.

The computer program product of the present invention may be such thatthe above-mentioned compound is introduced into an indoor space as asolution containing the compound is heated to vaporize; whereas theabove-mentioned media are condensed particles which are divided into atleast one kind according to generation and extinction,high-concentration air, medium-concentration air, low-concentration air,a floor, a wall, and a ceiling which is divided into at least one kindaccording to compound concentration.

Preferably, in this case, the differential equation in the condensedparticles is a differential equation stating a relationship amongtemporal change of fugacity of the compound in the condensed particles,temporal change in volume of the condensed particles, amount oftransference of the compound between the condensed particles and anothermedium, and change in amount of degradation of the compound in thecondensed particles; the differential equation in the high-concentrationair is a differential equation stating a relationship among temporalchange of fugacity of the compound in the high-concentration air, amountof discharge of the compound, amount of transference of the compoundbetween the high-concentration air and another medium, and change inamount of degradation of the compound in the high-concentration air; thedifferential equation in the medium-concentration air is a differentialequation stating a relationship among temporal change of fugacity of thecompound in the medium-concentration air, amount of transference of thecompound between the medium-concentration air and another medium, andchange in amount of degradation of the compound in themedium-concentration air; the differential equation in thelow-concentration air is a differential equation stating a relationshipamong temporal change of fugacity of the compound in thelow-concentration air, amount of discharge of the compound outdoors,amount of transference of the compound between the low-concentration airand another medium, and change in amount of degradation of the compoundin the low-concentration air; the differential equation at the floor isa differential equation stating a relationship among temporal change offugacity of the compound at the floor, temporal change in volume of thefloor, amount of transference of the compound between the floor andanother medium, and change in amount of degradation of the compound atthe floor; the differential equation at the wall is a differentialequation stating a relationship among temporal change of fugacity of thecompound at the wall, temporal change in volume of the wall, amount oftransference of the compound between the wall and another medium, andchange in amount of degradation of the compound at the wall; and thedifferential equation at the ceiling is a differential equation statinga relationship among temporal change of fugacity of the compound at theceiling, temporal change in volume of the ceiling, amount oftransference of the compound between the ceiling and another medium, andchange in amount of degradation of the compound at the ceiling.

The computer program product of the present invention may be such thatthe above-mentioned compound is introduced into an indoor space as asolution containing the compound is sprayed over the whole floor; whilethe above-mentioned media are suspended particles which are divided intoat least one kind according to size, indoor air, a floor, a wall, and aceiling.

Preferably, in this case, the differential equation in the suspendedparticles is a differential equation stating a relationship amongtemporal change of fugacity of the compound in the suspended particles,temporal change in volume of the suspended particles, amount oftransference of the compound between the suspended particles and anothermedium, and change in amount of degradation of the compound in thesuspended particles; the differential equation in the indoor air is adifferential equation stating a relationship among temporal change offugacity of the compound in the indoor air, amount of discharge of thecompound outdoors, amount of transference of the compound between theindoor air and another medium, and change in amount of degradation ofthe compound in the indoor air; the differential equation at the flooris a differential equation stating a relationship among temporal changeof fugacity of the compound at the floor, temporal change in volume ofthe floor, amount of attachment of the suspended particles to the floor,amount of transference of the compound between the floor and anothermedium, and change in amount of degradation of the compound at thefloor; the differential equation at the wall is a differential equationstating a relationship among temporal change of fugacity of the compoundat the wall, temporal change in volume of the wall, amount of attachmentof the suspended particles to the wall, amount of transference of thecompound between the wall and another medium, and change in amount ofdegradation of the compound at the wall; and the differential equationat the ceiling is a differential equation stating a relationship amongtemporal change of fugacity of the compound at the ceiling, temporalchange in volume of the ceiling, amount of attachment of the suspendedparticles to the ceiling, amount of transference of the compound betweenthe ceiling and another medium, and change in amount of degradation ofthe compound at the ceiling.

The computer program product of the present invention may be such thatthe floor is constituted by a rug having ears of fiber, whereas a spacebetween the ears is added to the above-mentioned media.

Preferably, in this case, the differential equation in the space betweenthe ears is a differential equation stating a relationship amongtemporal change of fugacity of the compound in the space between theears, temporal change in volume of the solution containing the compoundin the space between the ears, amount of attachment of the compound intothe space portion between the ears by falling, amount of transference ofthe compound between the space portion between the ears and anothermedium, and change in amount of degradation of the compound in the spaceportion between the ears.

Even in the case where a rug having ears of fiber is spread on thefloor, when the space between the ears is further added to the media,the behavior of the compound can be simulated accurately, thus allowingvarious kinds of simulations to be performed.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a flowchart showing a method of simulating an indoor behaviorof a pesticidal compound in accordance with an embodiment of the presentinvention;

FIG. 2 is an explanatory view showing a model of indoor environment inthe case where an indoor behavior of a compound is performed in thefirst embodiment of the present invention;

FIG. 3A is a graph showing temporal change of concentration in indoorair;

FIG. 3B is an explanatory view in the case where mean concentration inindoor air is determined by use of the graph in FIG. 3A;

FIG. 4A is a graph showing temporal change in residual amount;

FIG. 4B is an explanatory view in the case where mean residual amount isdetermined by use of the graph in FIG. 4A;

FIG. 5 is a flowchart showing a method of setting an estimation nicktime width;

FIG. 6A is an explanatory view showing a modeled state of a carpet inthe case where an indoor behavior of a pesticidal compound is estimatedin accordance with the second embodiment of the present invention;

FIG. 6B is an enlarged view of a carpet fiber in the case where anindoor behavior of a pesticidal compound is estimated in accordance withthe second embodiment of the present invention;

FIG. 6C is an enlarged view of a space portion of the carpet in the casewhere an indoor behavior of a pesticidal compound is estimated inaccordance with the second embodiment of the present invention;

FIG. 7 is a graph showing temporal change of concentration in the air inExample 1 in the above-mentioned first embodiment;

FIG. 8A is a graph showing temporal change in concentration in the airin the case where ventilation rate is changed in Example 2;

FIG. 8B is a graph showing temporal change in concentration in the airin the case where a window is opened and closed in Example 3;

FIG. 9A is a graph showing temporal change in residual amount on thefloor in Example 1;

FIG. 9B is a graph showing temporal change in residual amount on thewall and ceiling in Example 1;

FIG. 10A is a graph comparing actually measured values of concentrationin the air and their simulation results in Example 1;

FIG. 10B is a graph comparing actually measured values of residualamount at the spraying site, floor, wall, and ceiling and theirsimulation results in Example 1;

FIG. 11 is an explanatory view showing a modeled state of indoorenvironment in the case where an indoor behavior of a compound isestimated in the third embodiment of the present invention;

FIG. 12A is a graph comparing actually measured values of concentrationin the air and their simulation results in Examples 6 to 10;

FIG. 12B is a graph comparing actually measured values of concentrationin the air and their simulation results in Examples 6 to 10;

FIG. 12C is a graph comparing actually measured values of residualamount on the floor and ceiling and their simulation results in Example6;

FIG. 13A is an explanatory view showing a modeled state of a carpet inthe case where an indoor behavior of a pesticidal compound is estimatedin accordance with the fourth embodiment of the present invention;

FIG. 13B is an enlarged view of a carpet fiber in the case where anindoor behavior of a pesticidal compound is estimated in accordance withthe fourth embodiment of the present invention;

FIG. 13C is an enlarged view of a space portion of the carpet in thecase where an indoor behavior of a pesticidal compound is estimated inaccordance with the fourth embodiment of the present invention;

FIG. 14 is an explanatory view showing an example of size of a typicalroom, together with an airflow;

FIG. 15 is an explanatory view showing a modeled state of indoorenvironment in the case where an indoor behavior of a compound isestimated in the fifth embodiment of the present invention;

FIG. 16A is an explanatory view showing a modeled state of indoorenvironment in the case where an indoor behavior of the compound isestimated in the fifth embodiment of the present invention;

FIG. 16B is an enlarged view of an electric heating evaporator in thefifth embodiment of the present invention;

FIG. 17 is an explanatory view showing a modeled state of indoorenvironment in the case where an indoor behavior of a compound isestimated in the seventh embodiment of the present invention;

FIG. 18 is an explanatory view showing a falling state of a particlezone;

FIG. 19 is a configurational view of a storage medium 20 employed ineach of the above-mentioned embodiments of the present invention;

FIG. 20 is a configurational view of an information processing apparatusfor operating a program stored in the storage medium 20; and

FIG. 21 is a configurational view of the information processingapparatus for operating a program stored in the storage medium 20.

BEST MODES FOR CARRYING OUT THE INVENTION

(1) First Embodiment

With reference to the drawings, the first embodiment of the presentinvention will be explained in the following.

The method of simulating an indoor behavior of a pesticidal compound(hereinafter simply referred to as compound) contained in a chemical(solution) such as insecticide in accordance with this embodimentestimates, for example, the behavior of the compound when the chemicalis residually sprayed in order to exterminate indoor vermin such ascockroach. Here, residual spraying refers to a process in which achemical is sprayed to a local site such as the boundary between a floorand a wall. The chemical encompasses all kinds of insecticides and thelike, including pyrethroid insecticidal compounds, organophosphoruscompounds, carbamate compounds, and insect growth restrainers (IGR).

First, as shown in FIG. 2, an environment is classified into seven kindsof media consisting of spraying site 1, large particles (suspendedparticles) 2, small particles (suspended particles) 3, whole indoor air4, floor 5, wall 6, and ceiling 7.

When a chemical is sprayed to the boundary between the floor 5 and thewall 6, part of the chemical attaches to the spraying site 1, whereasthe rest dissipates into the air as large and small particles 2 and 3.The chemical attached to the spraying site 1 not only infiltrates intothis site but also evaporates. On the other hand, among the large andsmall particles 2 and 3, the smaller particles 3, due to their weight,scatter higher than the larger particles 2. When these particles attachonto interior materials of the floor 5, wall 6, and ceiling 7, thecompound in the particles moves into the air 4 after infiltrating intothe interior materials or is degraded by light or oxidation. Such largeand small particles 2 and 3 and evaporated chemical have decreased dueto ventilation of the room.

Simultaneous differential equations concerning Fugacity of the compoundin the above-mentioned seven kinds of media are formed and are solved byRunge-Kutta-Gill method, whereby the indoor behavior of the compound inthe chemical when the chemical is residually sprayed, i.e., compounddistribution in the room, and temporal change in amount of attachment tothe spraying site 1, floor 5, wall 6, or ceiling 7 are estimated andanalyzed.

Here, since the floor 5 mainly comprises three kinds, i.e., tatami,flooring, or carpet (rug), the differential equation is formed so as tocorrespond to the kind of floor. Explained in this embodiment is thecase where the floor 5 is made of flooring.

With reference to FIG. 1, a method of simulating an indoor behavior ofthe compound will be explained. The simulation method in accordance withthis embodiment can be mainly divided into a step of dividing an indoorenvironment into predetermined media and forming a differential equationconcerning a fugacity of the compound in each medium (S1 to S2); a stepof determining the fugacity of the compound in each medium from thedifferential equation (S3); a step of determining the indoor behavior ofthe compound from the fugacity of the compound in each medium (S4); astep of changing, in response to a fluctuation in mass balance of thecompound indoors, a minute time unit used when solving the differentialequation (S21 to S35, see FIG. 5); and a step of evaluating safety ofthe compound with respect to a human body according to the indoorbehavior of the compound (S5 to S17).

First, at step (hereinafter abridged as S) 1, a primary condition isinputted. The primary condition comprises physicochemical properties ofthe compound (see Table 1), indoor environmental behavior properties ofthe compound (see Table 2), indoor environment (see Table 3), andproduct properties (see Table 4).

TABLE 1 PHYSIOCHEMICAL PROPERTY OF COMPOUND SYMBOL EXAMPLE OF VALUEMOLECULAR WEIGHT — 350.46 [g/mole] SPECIFIC GRAVITY ρ  1.11 [g/cm³]VAPOR PRESSURE P^(S) 1.60 × 10⁻⁴ [Pa] WATER SOLUBILITY C^(S) 6.28 × 10⁻³[mole/m³] OCTANOL/WATER K_(OW) 7.59 × 10⁴ DISTRIBUTION COEFFICIENT

TABLE 2 INDOOR ENVIRONMENTAL BEHAVIOR PROPERTY OF COMPOUND SYMBOLEXAMPLE OF VALUE DEGRADATION HALF-LIFE IN SPRAYING SITE τ_(I) 13 [day]PARTICLE τ_(i)(i = 2,3) 7.7 [h] AIR τ₄ 7.7 [h] FLOOR τ₅  13 [day] (INCASE OF FLOORING) WALL/CEILING τ_(j) (j = 6,7)  31 [day] (IN CASE OFWALLPAPER)

TABLE 3 SYM- EXAMPLE OF INDOOR ENVIRONMENT BOL VALUE OIL ROOM SIZE V₄23.3 [m³] BASE TEMPERATURE T 895 [K] (=25 [° C.]) RELATIVE HUMIDITY φ 60[% RH] ABSOLUTE HUMIDITY H 1.19 × 10⁻² (kg-H₂O/kg-dry air] VENTILATIONRATE G 1.58 [1/h] INDOOR VAPOR P∞ 0 [Pa] PRESSURE IN PARTICLE -CONSTITUTING SOLVENT AIR DIFFUSION Dair 8.64 × 10⁻² [m²/h] COEFFICIENTOIL COMPONENT 0.04 (IN CASE CONTENT OF FLOORING) 0.46 (IN CASE OFTATAMI) 0.3 (IN CASE OF WALLPAPER) WATER WET-BULB T_(d) 292.5 [K] BASETEMPERATURE VAPOR PRESSURE OF P∞ 1.89 × 10^(3 [Pa]) WATER HERE, V₄ = L₄× W₄ × HEIGHT (= 3.6 m × 2.7 m × 2.4 m)

TABLE 4 EXAMPLE OF PRODUCT PROPERTY SYMBOL VALUE OIL COMPOUND CONTENTC_(a) 6.74 × 10³ [g/m³] BASE COMPOUND EMISSION A_(a) 8.19 × 10⁻⁴ [mole]AMOUNT PARTICLE CONSTITUT- O_(a) 4.26 × 10⁻⁵ [m³] ING SOLVENT EMISSIONAMOUNT PARTICLE- CONSTITUTING SOLVENT PROPERTY VAPOR PRESSURE P_(d) 2.72[Pa] MOLECULAR WEIGHT M_(d) 184.37 [g/mole] SPECIFIC GRAVITY ρd 7.56 ×10⁻⁶[g/m³] RATIO OF ATTACH- — 60 [%] MENT TO SPRAYING SITE DIAMETERS OFSUS- d₀₂ 20 [μm] PENDED PARTICLES d₀₃  5 [μm] (2 KINDS) DISTRIBUTIONS OF— 30 [%] SUSPENDED PARTICLES (LARGE (2 KINDS) PARTICLE) — 10 [%] (SMALLPARTICLE) SPRAYING SITE AREA A_(t) (3.6 + 2.7) × 0.1 × 4 [m²] WATERPARTICLE - CONS- BASE TITUTING SOLVENT PROPERTY VAPOR PRESSURE P_(d)2.26 × 10³ [Pa] MOLECULAR WEIGHT M_(d) 18 [g/mole] SPECIFIC GRAVITYρ_(d) 1 × 10⁶ [g/m³]

Subsequently, using the primary condition, a secondary condition isdetermined by calculation (S2). The secondary condition comprises atemporally unchangeable definite factor condition (see Table 5)determined by the primary condition alone, and a temporal changecondition accompanying a temporal change (see Table 6). Theircalculations will be explained later in detail.

TABLE 5 DEFINITE FACTOR CONDITION SYMBOL EVAPORATION CONSTANT OFSUSPENDED α PARTICLE VOLUME RATIO OF COMPOUND IN PRODUCT R_(a) DIFFUSIONCOEFFICIENT OF COMPOUND IN AIR D_(ca) SURFACE AREA OF FLOOR/WALL/CEILINGAj (j = 5,6,7) DIFFUSION COEFFICIENT OF FLOOR/WALL/ D_(c) CEILING RATIOOF SUSPENDED PARTICLE FALLING TO γ1 SPRAYING SITE RATIO OF SUSPENDEDPARTICLE ATTACHING TO γj (j = 5,6,7) FLOOR/WALL/CEILING FUGACITYCAPACITY OF SPRAYING SITE Z_(I) SUSPENDED PARTICLE Z_(i) (i = 2,3) AIRZ₄ FLOOR/WALL/CEILING Zj (j = 5,6,7) DEGRADATION CONSTANT OF SPRAYINGSITE K_(I) SUSPENDED PARTICLE K_(i) (i = 2,3) AIR K₄ FLOOR K₅WALL/CEILING Kj (j = 6,7) HERE, AN EXAMPLE OF DIFFUSION COEFFICIENTACCORDING TO EXAMPLES OF VALUES IN TABLE1 IS 1.36 × 10⁻¹¹ [m²/h] .

TABLE 6 TEMPORAL CHANGE CONDITION SYMBOL SUSPENDED PARTICLE DIAMETERd_(i) (i = 2,3) FALLING SPEED v_(i) (i = 2,3) FLOATING NUMBER n_(i) (i =2,3) FLOATING HEIGHT H_(i) (i = 2,3) TRANSFERENCE SPEED OF COMPOUND INSPRAYING SITE k_(I) SUSPENDED PARTICLE k_(i) (i = 2,3) AIR k₄FLOOR/WALL/CEILING k_(j) (j = 5,6,7) TRANSFERENCE COEFFICIENT OFCOMPOUND D_(I4) BETWEEN SPRAYING SITE AND AIR TRANSFERENCE COEFFICIENTOF COMPOUND D_(i4 (i = 2,3)) BETWEEN SUSPENDED PARTICLE AND AIRTRANSFERENCE COEFFICIENT OF COMPOUND D_(4j) (j = 5,6,7) BETWEEN AIR ANDFLOOR/WALL/CEILING VOLUME OF SPRAYING SITE V_(I) VOLUME OF SUSPENDEDPARTICLE V_(i) (i = 2,3) VOLUME OF FLOOR/WALL/CEILING V_(j) (j = 5,6,7)

Using the secondary condition, seven kinds of Fugacity are calculated(S3). Namely, seven kinds of differential equations concerning thespraying site 1, large and small particles 2 and 3, air 4, floor 5, wall6, and ceiling 7 are simultaneously formed and are solved byRunge-Kutta-Gill method, whereby seven kinds of Fugacity are computedover time. Here, an estimation nick time width (minute time unit) setwhen solving the differential equations is automatically set so as to bevaried in response to a fluctuation in mass balance of the compound.

At S4, using thus computed Fugacity (f₃, f₄) of the small particles 3and air 4, together with Fugacity (f₂) of the large particles 2 whennecessary, temporal concentration of the compound in the indoor air iscomputed; whereas temporal residual amounts of the compound to thespraying site 1 and floor 5 are computed by use of Fugacity (f₁, f₅) ofthe spraying site 1 and floor 5.

At S5, it is judged whether or not to perform safety evaluation in thecase where the chemical is inhaled. If the safety evaluation ininhalation is to be performed, then an estimated exposure amount ininhalation indicating a degree of exposure upon inhalation of thecontaminated air is computed by use of the above-mentioned temporalconcentration in the indoor air (S6). Thereafter, an inhalation safetycoefficient is computed according to the estimated exposure amount ininhalation (S7). At S8, the inhalation safety coefficient is comparedwith a reference value defined in each country. If the inhalation safetycoefficient exceeds the reference value, it is judged that “there is noproblem in safety.” By contrast, if the inhalation safety coefficient islower than the reference value at S8, it is judged that “there is aproblem in safety,” and the operation returns to S1, where alteration ofthe primary condition such as alteration of compound, alteration ofchemical formulation, alternation of using condition, or the like isconsidered.

If the safety evaluation in inhalation is not selected at S5, calculatedis an estimated amount of percutaneous exposure indicating to whatextent the skin is exposed in contact with the spraying site 1 or floor5 to which the chemical is attached (S9). Thereafter, at S10, it isjudged whether to perform a percutaneous safety evaluation or not. Ifthe percutaneous safety evaluation is to be performed, a percutaneoussafety coefficient is computed according to the estimated percutaneousexposure amount (S11). At S12, as with the safety evaluation ininhalation, the percutaneous safety coefficient is compared with areference value defined in each country, whereby the safety isevaluated. If there is a problem in safety at S12, the operation returnsto S1, where alteration of the primary condition is considered.

If the percutaneous safety evaluation is not selected at S10, calculatedaccording to the estimated percutaneous exposure amount is an estimatedoral exposure amount indicating the degree of exposure in the case wherethe chemical attached to a hand or the like is taken orally (S13).Subsequently, according to the estimated oral exposure amount, an oralsafety coefficient is computed (S14). This oral exposure may occur, inparticular, when an infant puts a chemical-attached hand into the mouth.At S15, as with the safety evaluation in inhalation, the oral safetycoefficient is compared with a reference value defined in each country,whereby the safety is evaluated. If there is a problem in safety at S15,the operation returns to S1, where alteration of the primary conditionis considered.

Finally, if it is judged to be safe at S8, S12, or S15, overall safetyis evaluated. Here, the sum of respective reciprocals of the previouslydetermined inhalation safety coefficient, percutaneous safetycoefficient, and oral safety coefficient is determined, and thereciprocal of thus determined value is defined as an overall safetycoefficient (S16). This overall safety coefficient is compared with areference value, whereby an evaluation similar to the previous safetyevaluation is effected (S17).

In the following, the above-mentioned steps of S2 to S4, S6, S7, S9,S11, S13, and S14 will be explained in detail.

(i) Secondary Condition Calculation (S2)

Calculations of the definite factor condition shown in Table 5 and thetemporal change condition shown in Table 6 will be explained.

According to surface temperature (T_(d)) of particles, properties ofparticle-constituting solvent (vapor pressure P_(d), molecular weightM_(d), and specific gravity ρ_(d)), and indoor environment (airdiffusion coefficient D_(air), vapor pressure P^(∞), and roomtemperature T^(∞)), the evaporation constant (α) of the large and smallparticles 2 and 3 is defined as follows: $\begin{matrix}{\alpha = {\frac{4D_{air}M_{d}}{R\quad \rho_{d}}\left( {\frac{P_{d}}{T_{d}} - \frac{P^{\infty}\quad}{T^{\infty}\quad}} \right)}} & (1)\end{matrix}$

wherein R is a gas constant.

Here, the upper parts of the above-mentioned Tables 3 and 4 exemplifythe case where the residually sprayed aerosol is of oil base. In thiscase, T^(∞) (temperature at the site far from particles) and T_(d) areset to room temperature (T), whereas P^(∞) (vapor pressure of oil at thesite far from particles) is set to zero.

In the case where the residually sprayed aerosol is of water base, it isnecessary for P_(d), M_(d), ρ_(d), T_(d), and P^(∞) in expression (1) tobe changed to values based on properties of water. Specifically, theabove-mentioned factor values when the room temperature (T) is 298 [K](=25° C.) and the relative humidity is 60[% RH] are exemplified in thelower parts of Tables 3 and 4.

Here, T_(d) can be determined, according to the room temperature (T) andrelative humidity (H), from “mass-based humidity table” disclosed in“Kagaku Kikai no Riron to Keisan (Theory and Calculation of ChemicalMachines)” (Second Edition) (Saburo Kamei ed., Sangyo Tosho) or thelike. On the other hand, P_(d) and P^(∞) can be computed from thefollowing expressions:

log₁₀ P _(d)=10.23−1750/(T _(d)−38)

log₁₀ P ^(∞)=8.23−1750/(T−38)+log₁₀ψ

wherein ψ is an indoor relative humidity.

From the vapor pressure (P^(s)), water solubility (C^(s)), andoctanol/water distribution coefficient (K_(ow)) of the compound, andfrom the oil component content (ρ₁) of the floor or wall constitutingthe spraying site 1, Fugacity capacity (Z₁) of the spraying site 1 isexpressed as:

Z ₁=ρ₁ K _(OW) C ^(S) /P ^(S)  (2)

From the vapor pressure (P^(s)) of the compound and the surfacetemperature (T_(d)) of particles, Fugacity capacity (Z_(i), i=2, 3) ofthe large and small particles 2 and 3 is expressed as: $\begin{matrix}{{Z_{i} = \frac{6 \times 10^{6}}{P_{L}^{S}{RT}_{d}}}{P_{L}^{S} = {P^{S}\exp \left\{ {6.79\left( {{T_{M}/T_{d}} - 1} \right)} \right\}}}} & (3)\end{matrix}$

Though the vapor pressure of the compound in a liquid state (P_(L) ^(s))is computed by use of the melting point T_(M) of the harmful materialand T_(d) here; in the case where T_(M) cannot be obtained, P_(L) ^(s)may be set identical to the vapor pressure of the compound in a solidstate (P^(s)).

From the room temperature (T), Fugacity capacity (Z₄) of the air 4 isexpressed as follows: $\begin{matrix}{Z_{4} = \frac{1}{RT}} & (4)\end{matrix}$

From the vapor pressure (P^(s)), water solubility (C^(s)), andoctanol/water distribution coefficient (K_(ow)) of the compound, andfrom the particle-constituting solvent component content (ρ_(j), j=5, 6,7) of the material constituting the floor 5, wall 6, and ceiling 7,Fugacity capacity (Z_(j), j=5, 6, 7) of the floor 5, wall 6, and ceiling7 is expressed as:

Z _(j)=ρ_(j) K _(OW) C ^(S) /P ^(S)  (5)

Though the ratio (γ_(j)) of the large and small particles 2 and 3attaching to the floor 5, wall 6, and ceiling 7 may be assumed to besuch that 100% of them attach to the floor 5 from viewpoint of safetyevaluation, it may be set, for example, floor:wall:ceiling=97:2:1 inview of the actually measured values in the past.

The ratio (γ₁) of the large and small particles 2 and 3 falling to thespraying site 1 is determined by the above-mentioned ratio (γ_(j)), andthe area (A₁) occupied by the spraying site 1 with respect to the sizeof the room (V₄).

The diffusion coefficient (D_(c)) of the compound in the floor 5, wall6, and ceiling 7 can be computed as follows. Namely, D_(c) can bedetermined when the diffusion coefficient (D_(ca)) of the compound inthe air is multiplied by 10⁻⁹, whereas D_(ca) can be computed fromproperties of the compound (e.g., structural formula, molecular weight,and the like) according to Wike and Lee method (“Handbook of ChemicalProperty Estimation Methods,” McGraw-Hill Book Company, 1982), forexample.

Mainly generated in the seven kinds of media are degradation reactionscaused by light and oxidation. The degradation constant (K₁) of thespraying site 1, degradation constant (K_(i), i=2, 3) of the large andsmall particles 2 and 3, degradation constant (K₄) of the air 4,degradation constant (K₅) of the floor 5, and degradation constant(K_(j), j=6, 7) of the wall 6 and ceiling 7 are defined by use ofdegradation half-life (τ₁), (τ_(i)), (τ₄), (τ₅), or (τ_(j)) as:$\begin{matrix}\left. \begin{matrix}{K_{1} = {0.693/\tau_{1}}} \\{K_{i} = {0.693/\tau_{i}}} \\{K_{4} = {0.693/\tau_{4}}} \\{K_{5} = {0.693/\tau_{5}}} \\{K_{j} = {0.693/\tau_{j}}}\end{matrix} \right\} & (6)\end{matrix}$

Here, among the degradation half-lives shown in the above-mentionedTable 2, it is difficult to actually measure the degradation half-life(τ₄) of the compound in the air, whereby it is not usually easy for thedegradation constant (K₄) to be determined. Therefore, when the actuallymeasured value is unavailable, it may be determined as being computed byAtmospheric Oxidation program (Atkinson et al., 1984, Chem. Rev. Vol.84, pp. 437-470) using the structural formula of the compound. Also, thedegradation constant in the particles and in the interior materials(floor 5, wall 6, and ceiling 7) may be set to zero in view of thesafety of inhabitants when the actually measured values are unavailable.

Since the volume of particles decreases over time due to evaporation ofthe particle-constituting solvent component, during the evaporation ofparticle-constituting solvent component, using the diameter (d_(0i),i=2, 3) of particles immediately after spraying (t=0) and theevaporation constant (α) determined from expression (1), the diameter(d_(i), i=2, 3) of the large and small particles 2 and 3 at time t isrepresented as shown in the following expression (7):

d _(i) ={square root over (d_(0i) ²−2αt)}  (7)

d _(i) ={square root over (R_(a))} d _(0i)  (7′)

By contrast, the diameter (d_(i)) of particles after completeevaporation of the particle-constituting solvent component isrepresented as shown in the above expression (7′) by use of the ratio ofvolume of the compound in the product (R_(a)) and the diameter (d_(0i))of particles immediately after spraying.

From the compound content (C_(a)) and specific gravity (ρ) of thecompound, the ratio of volume of the compound in the product (R_(a)) isexpressed as C_(a)/ρ.

Since movement of the particles is under the control of gravity and airresistance, according to Stokes' law using the specific gravity (ρ_(d))of the particle-constituting solvent and the diameter (d_(i)) ofparticles determined by expression (7), the falling speed (v_(i), i=2,3) of the large and small particles 2 and 3 before complete evaporationof the particle-constituting solvent component is represented by thefollowing expression (8): $\begin{matrix}{v_{i} = {{\frac{\rho_{d}{gS}_{c}}{18\eta}d_{i}^{2}} = {\beta \left( {d_{0i}^{2} - {2\alpha \quad t}} \right)}}} & (8) \\{S_{c} = {1 + {\frac{2}{7.6 \times 10^{7}d_{i}}\left\{ {6.32 + {2.01{\exp \left( {{- 8.322} \times 10^{6}d_{i}} \right)}}} \right\}}}} & \left( 8^{\prime} \right) \\{v_{i} = {\left( {\rho/\rho_{d}} \right)\beta \quad d_{i}^{2}}} & \left( 8^{''} \right)\end{matrix}$

wherein g is gravitational acceleration, η is the coefficient ofviscosity of the air 4, S_(c) is a sliding correction coefficient, and,β is a speed coefficient. Here, while particles do not conform to theStokes' law when they become small, the sliding correction coefficient(S_(c)) which is a coefficient for correcting this phenomenon, isrepresented by the above expression (8′) according to the diameter(d_(i)) of particles determined by expression (7).

On the other hand, the falling speed (v_(i)) of the particles after thecomplete evaporation of particle-constituting solvent component isrepresented by the above expression (8″) using the specific gravity (ρ)of the compound, specific gravity (ρ_(d)) of the particle-constitutingsolvent, speed coefficient (β), and diameter (d_(i)) of particlesdetermined by expression (7′).

From transference speed (k₄) of the compound in the air 4, which will beexplained later, floating height of particles (H_(i)), size of the room(V₄=L₄×W₄×height), and the falling speed (v_(i)) of particles determinedby expression (8) or (8″), the number of floating large and smallparticles 2 and 3 (n_(i), i=2, 3) is expressed as: $\begin{matrix}{\frac{n_{i}}{t} = {{{- \frac{n_{i}}{H_{i}}}v_{i}} - {\frac{n_{i}}{L_{4}}k_{4}}}} & (9)\end{matrix}$

Here, the floating height (H_(i)) of particles refers to the maximumheight of the particle distribution from the floor 5 after the particlesare reflected by the spraying site 1 and then are suspended in the casewhere the chemical is sprayed to the spraying site 1. It is positionedhigher as the particles are finer.

Using the diffusion coefficient (D_(c)) of compound in the floor 5, wall6, and ceiling 7, the transference speed (k₁) of the compound in thespraying site 1 is expressed as (D_(c)/t)^(0.5).

From the transference speed (k₄) of the compound in the air 4 indicatedin the following, the transference speed (k_(i), i=2, 3) of the compoundin the large and small particles 2 and 3 is expressed as k₄/100.

From the ventilation rate (G), the transference speed (k₄) of thecompound in the air 4 is expressed as GV₄/A₄. Here, the above-mentionedA₄ is the cross-sectional area of the room with respect to the movingdirection of the air 4 (arrowed direction in FIG. 2).

Using the diffusion coefficient (D_(c)) of compound in the floor 5, wall6, and ceiling 7, the transference speed (k_(j), j=5, 6, 7) of thecompound in the floor 5, wall 6, and ceiling 7 is expressed as(D_(c)/t)^(0.5).

From the transference coefficient (k₁) of the compound in the sprayingsite 1, transference speed (k₄) of the compound in the air 4, area(A_(t)) of the spraying site 1, falling speed (v_(i)) of particlesdetermined by expression (8) or (8″), Fugacity capacity (Z₁) of thespraying site 1 determined by expression (2), and Fugacity capacity (Z₄)of the air 4 determined by expression (4), the transference coefficient(D₁₄) of the compound between the spraying site 1 and the air 4 isrepresented as follows: $\begin{matrix}{D_{14} = \frac{1}{{1/\left( {k_{1}A_{1}A_{t}Z_{1}} \right)} + {1/\left( {k_{4}A_{1}A_{t}Z_{4}} \right)}}} & (10)\end{matrix}$

From the transference speed (k₁) of the compound in the large and smallparticles 2 and 3, transference speed (k₄) of the compound in the air 4,diameter (d_(i)) of particles determined by expression (7) or (7′),Fugacity capacity (Z_(i)) of particles determined by expression (3), andFugacity capacity (Z₄) of the air 4 determined by expression (4), thetransference coefficient (D_(i4), i=2, 3) between the large and smallparticles 2 and 3 and the air 4 is represented as follows:$\begin{matrix}{D_{i4} = \frac{1}{{1/\left( {k_{i}A_{i}Z_{i}} \right)} + {1/\left\{ {\left( {k_{4} + v_{i}} \right)A_{i}Z_{4}} \right\}}}} & (11)\end{matrix}$

wherein A_(i)(=πd_(i) ²) is the surface area of particles.

From the transference speed (k₄) of the compound in the air 4,transference speed (k_(j)) of the compound in the floor 5, wall 6, andceiling 7, surface area (A_(j)) of the floor 5, wall 6, and ceiling 7,Fugacity capacity (Z₄) of the air 4 determined by expression (4), andFugacity capacity (Z_(j)) of the floor 5, wall 6, and ceiling 7determined by expression (5), the transference coefficient (D_(4j), j=5,6, 7) of the compound between the air 4 and the floor 5, wall 6, andceiling 7 becomes: $\begin{matrix}{D_{4j} = \frac{1}{{1/\left( {k_{4}A_{j}Z_{4}} \right)} + {1/\left( {k_{j}A_{j}Z_{j}} \right)}}} & (12)\end{matrix}$

Here, the surface area (A_(j)) of each of the floor 5, wall 6, andceiling 7 is determined by the size of the room (V₄=L₄×W₄×height) andthe area (A_(t)) of the spraying site 1.

The volume (V₁) of the spraying site 1 is determined by the diffusioncoefficient (D_(c)) in the floor 5, wall 6, and ceiling 7.

Using the diameter (d_(i)) of suspended particles determined byexpression (7) or (7′) and the evaporation constant (α) determined byexpression (1), the volume change (dV_(i)/dt) of the large and smallparticles 2 and 3 is represented as: $\begin{matrix}{\frac{V_{i}}{t} = {{- \frac{\pi}{2}}\alpha \quad d_{i}}} & (13)\end{matrix}$

Namely, as the oil component or moisture in the large and smallparticles 2 and 3 evaporates over time, their volume (V_(i), i=2, 3)decreases.

Assuming that each of the floor 5, wall 6, and ceiling 7 beforeresidually spraying the chemical is like a thin film and that, as thechemical infiltrates into the film, its thickness increases so as toenhance the volume thereof; from the surface area (A_(j)) of the floor 5wall 6, and ceiling 7 and diffusion coefficient (D_(c)) of the compoundin the floor 5, wall 6, and ceiling 7, the volume (V_(j), j=5, 6, 7) offloor 5, wall 6, and ceiling 7 is indicated as follows:

V _(j)=2{square root over (D _(c) t)}A _(j)  (14)

(ii) Fugacity Calculation (S3)

The behavior of the compound in the spraying site 1 is expressed in theform of differential equation concerning Fugacity (f₁) as:$\begin{matrix}\begin{matrix}{\frac{f_{1}}{t}V_{1}Z_{1}} & = & {{{- \sqrt{D_{c}/t}}A_{1}Z_{1}f_{1}} +} & {V\text{-}{change}} \\{F\text{-}{change}} & \quad & {{\gamma_{1}{\sum\limits_{i = 2}^{3}\quad {n_{i}V_{i}Z_{i}f_{i}}}} -} & {{Deposition}(i)} \\\quad & \quad & {{D_{14}\left( {f_{1} - f_{4}} \right)} -} & {{Transference}(1)} \\\quad & \quad & {K_{1}V_{1}Z_{1}f_{1}} & {Degradation}\end{matrix} & (15)\end{matrix}$

Here, the terms of V-change, Deposition (i), Transference (1), andDegradation respectively indicate volume change (increase over time) ofthe spraying site 1, attachment accompanying the falling of the largeand small particles 2 and 3, amount of transference of the compoundbetween the spraying site 1 and the air 4, and change in amount ofphotodegradation of the compound.

The behavior of the compound in the large and small particles 2 and 3 isexpressed in the form of differential equation concerning Fugacity(f_(i), i=2, 3) as: $\begin{matrix}\begin{matrix}{{\frac{f_{i}}{t}V_{i}Z_{i}} = {{\frac{\pi}{2}\alpha \quad d_{i}Z_{i}f_{i}} -}} & {{V\text{-}{change}}} \\{{F\text{-}{change}{\quad }{D_{14}\left( {f_{1} - f_{4}} \right)}} -} & {{{Transference}(1)}} \\{{{D_{i4}\left( {f_{i} - f_{4}} \right)} -}} & {{{Transference}(4)}} \\{{K_{i}V_{i}Z_{i}f_{i}}} & {{Degradation}}\end{matrix} & (16)\end{matrix}$

Here, the terms of V-change, Transference (1), Transference (4), andDegradation respectively indicate volume change (decrease over time) ofthe large and small particles 2 and 3, amount of transference of thecompound between the spraying site 1 and the air 4, amount oftransference of the compound between the large and small particles 2 and3 and the air 4, and change in amount of photodegradation of thecompound.

The behavior of the compound in the air 4 is expressed in the form ofdifferential equation concerning Fugacity (f₄) as: $\begin{matrix}\begin{matrix}{{\frac{f_{4}}{t}V_{4}Z_{4}} = {{{- {GV}_{4}}Z_{4}f_{4}} -}} & {{Ventilation}} \\{{F\text{-}{change}{\quad }{D_{14}\left( {f_{4} - f_{1}} \right)}} -} & {{{Transference}(1)}} \\{{{\sum\limits_{i = 2}^{3}{n_{i}{D_{i4}\left( {f_{4} - f_{i}} \right)}}} -}} & {{{Transference}(i)}} \\{{{\sum\limits_{j = 5}^{7}{D_{4j}\left( {f_{4} - f_{j}} \right)}} -}} & {{{Transference}(j)}} \\{{{K_{4}V_{4}Z_{4}f_{4}} -}} & {{Degradation}}\end{matrix} & (17)\end{matrix}$

Here, the terms of Ventilation, Transference (1), Transference (i),Transference (j), and Degradation respectively indicate amount ofdischarge of the compound outdoors, amount of transference of thecompound between the air 4 and the spraying site 1, amount oftransference of the compound between the air 4 and the large and smallparticles 2 and 3, amount of transference between the air 4 and thefloor 5, wall 6, and ceiling 7, and change in amount of photodegradationof the compound.

The behavior of the compound in the floor 5, wall 6, and ceiling 7 isexpressed in the form of differential equation concerning Fugacity(f_(j), j=5, 6, 7) as follows: $\begin{matrix}\begin{matrix}{{\frac{f_{i}}{t}V_{j}Z_{j}} = {{{- \sqrt{D_{c}/t}}A_{j}Z_{j}f_{j}} +}} & {{V\text{-}{change}}} \\{{F\text{-}{change}{\quad }\gamma_{j}{\sum\limits_{i = 2}^{3}{n_{i}V_{i}Z_{i}f}}} -} & {{{Deposition}(i)}} \\{{{D_{4j}\left( {f_{j} - f_{4}} \right)} -}} & {{{Transference}(4)}} \\{{K_{j}V_{j}Z_{j}f_{j}}} & {{Degradation}}\end{matrix} & (18)\end{matrix}$

Here, the terms of V-change, Deposition (i), Transference (4), andDegradation respectively indicate volume change (increase over time) ofthe floor 5, wall 6, and ceiling 7, attachment accompanying the fallingof the large and small particles 2 and 3, amount of transference of thecompound between the floor 5, wall 6, ceiling 7 and the air 4, andchange in amount of photodegradation of the compound.

The above-mentioned seven kinds of differential equations (15) to (18)are simultaneously formed and are solved by Runge-Kutta-Gill method, soas to compute Fugacity (f₁ to f₇).

When solving these simultaneous differential equations, it is necessaryto set an estimation nick time width (dt) which is a minute time unit.Namely, the estimation nick time width is used such that solutions ofthe simultaneous differential equations are initially determined at atime (t₀), and then solutions of the simultaneous differential equationsare determined at a time (t₀+dt) to which the estimation nick time widthis added. As solutions are obtained while estimation nick time widthsare successively added, temporally changing Fugacity can be determined.Theoretically, as the set time of the estimation nick time width isshorter, more accurate solutions can be obtained, though necessitating avery long calculation time. By contrast, when the set time is too long,solutions tend to diverge, thereby generating errors.

Therefore, in the present invention, the estimation nick time width isset shorter when a very large change occurs in a chemical, whereas it isset longer when there is no large change.

Specifically, mass balance is always confirmed such that the amount ofinput of the chemical and the resulting solution coincide with eachother, and the estimation nick time width is set longer when the massbalance does not fluctuate greatly, whereas it is set shorter when themass balance starts fluctuating. For example, when the fluctuation ofmass balance is set to an accuracy of ±5%, the estimation nick timewidth is always set so as to constantly satisfy the relationship of:

compound input amount/(existing amount+degrading amount+dischargingamount)=0.95 to 1.05

namely, such that the fluctuation of mass balance lies within the rangeof ±5%.

Here, the above-mentioned compound input amount is the compound emissionamount (A_(a)). Since the temporal amounts of compound in the sevenkinds of media are determined by the simultaneous differentialequations, they are summed up so as to compute the existing amount asshown in the following. Also, the degrading amount and dischargingamount are as follows: $\begin{matrix}\left. \begin{matrix}{{{existing}\quad {amount}} = {{V_{1}Z_{1}f_{1}} + {\sum\limits_{i = 2}^{3}{n_{i}f_{i}V_{i}Z_{i}}} + {\sum\limits_{k = 4}^{7}{f_{k}V_{k}Z_{k}}}}} \\{{{degrading}\quad {amount}} = {{K_{1}V_{1}Z_{1}f_{1}} + {\sum\limits_{i = 2}^{3}{K_{i}n_{i}f_{i}V_{i}Z_{i}}} + {\sum\limits_{k = 4}^{7}{K_{k}f_{k}V_{k}Z_{k}}}}} \\{{{discharging}\quad {amount}} = {{G\quad V_{4}Z_{4}f_{4}} + {\sum\limits_{i = 2}^{3}{G\quad n_{i}V_{i}Z_{i}f_{i}}}}}\end{matrix} \right\} & (19)\end{matrix}$

With reference to the flowchart of FIG. 5, the method of setting theestimation nick time width (dt) will be explained.

First, an initial value of estimation nick time width (dt) is inputted(S21). Then, an upper limit set value (e.g., 0.1[%]) which is the upperlimit of difference in mass balance, and a lower limit set value (e.g.,10⁻⁶[%]) which is the lower limit of difference in mass balance areinputted (S22). Thereafter, Fugacity and mass balance at t=t₀ arecalculated (S23 and S24), and Fugacity and mass balance at t=t+dt (ort₀+dt) are calculated (S25 and S26).

It is judged whether the fluctuation in mass balance is within the rangeof ±5% or not (S27). If the fluctuation in mass balance is within therange of ±5%, it is judged whether the difference between the massbalance at t=t (or t₀) and the mass balance at t=t+dt (or t₀+dt) is atleast the upper limit set value or not (S28). If it is judged to be atleast the upper limit set value at S28, then solutions become moreaccurate when the estimation nick time width (dt) is made shorter. Inthis case, the estimation nick time width (dt) is multiplied by ½ so asto change its setting (S29). When the difference is judged to be smallerthan the upper limit set value at S28, it is judged at S30 whether thedifference between the mass balance at t=t (or t₀) and the mass balanceat t=t+dt (or t₀+dt) is at most the lower limit set value or not.

When the mass balance difference is not greater than the lower limit setvalue at S30, since solutions are not influenced by longer estimationnick time width (dt), the estimation nick time width (dt) is doubled soas to change its setting (S31). Subsequently, it is judged whether theestimation nick time width (dt) changed at S31 is at most a maximumvalue (e.g., 0.1 [hour]) of estimation nick time width (dt) or not(S32). When the estimation nick time width (dt) is not greater than themaximum value at S32, since solutions do not diverge, the estimationnick time width (dt) set at S31 is used. When the estimation nick timewidth (dt) is greater than the maximum value at S32, since solutions maydiverge, the estimation nick time width (dt) is reset to the maximumvalue (S33). When the mass balance difference is greater than the lowerlimit set value at the above-mentioned S30, namely, when it lies betweenthe lower limit set value and upper limit set value, the calculationsare continued without changing the estimation nick time width (dt).

After the step of S29, S30, S32, or S33, the operation returns to S25 soas to effect calculation again, and this process is repeated till theaimed time is attained.

When the fluctuation in mass balance exceeds the range of ±5% at S27, onthe other hand, the mass balance fluctuation is so much that calculationis preferably effected with an estimation nick time width (dt) shorterthan that in the case where the fluctuation is within the range of ±5%.Accordingly, the calculation is stopped once (S34), the lower limit setvalue is reset to a lower level (S35), and then the operation returns tothe step of S23.

Thus, when the estimation nick time width is variably set without beingheld constant, while monitoring the mass balance fluctuation, Fugacitycan be computed accurately and efficiently.

(iii) Computation of Temporal Concentration in Indoor Air and ResidualAmount (S4)

The temporal concentration of the compound in the indoor air is computedwhen Fugacity (f₄) of the air, determined by the above-mentioned item(ii), multiplied by Fugacity capacity (Z₄), and Fugacity (f₃) of smallparticles multiplied by Fugacity capacity (Z₃) are summed up. Here, thelarge particles may be inhaled by a human body depending on the kind ofchemical. In such a case, calculation is effected by use of Fugacity(f₂) and (f₃) of large and small particles.

The residual amount of the compound is computed when Fugacity (f₁) ofthe spraying site 1 multiplied by Fugacity capacity (Z₁), and Fugacity(f₅) of the floor 5 multiplied by Fugacity capacity (Z₅) are summed up.Here, in the case where there is substantially no possibility of thespraying site 1 coming into contact with the skin, Fugacity (f₅) of thefloor 5 alone may be used for calculation.

(iv) Calculation of Estimated Exposure Amount in Inhalation andInhalation Safety Coefficient (S6 and S7)

The above-mentioned temporal concentration in the indoor air forms acurve shown in FIG. 3A, for example. This concentration curve isintegrated, an accumulated concentration of the compound during aspecific period (t₁ to t₂) is determined (see FIG. 3B), and the meanconcentration in the indoor air is computed from thus determined value.While an arbitrary period is set as the specific period depending on theobject, an appropriate period is usually set in view of the method ofuse of the product and the test period of toxicity data.

Then, according to the above-mentioned mean concentration in the indoorair, amount of respiration, and exposure time, the estimated exposureamount in inhalation is determined. Namely, calculation of:

estimated exposure amount in inhalation [mg/kg/day]=mean concentrationin indoor air [mg/m³]×amount of respiration [m³/kg/min]×exposure time[min/day]

is effected. Here, as the above-mentioned amount of respiration, apublished value or actually measured value may be used. Also, whenamounts of respiration are respectively set for adult and child, moreappropriate estimated exposure amounts in inhalation can be obtained. Inthe case where the inhaled harmful material is not totally absorbed intothe body but is partially discharged by respiration, a more appropriateestimated exposure amount in inhalation can be obtained when theinhalation ratio is taken into account.

The inhalation safety coefficient is computed from a non-influentialamount concerning inhalation toxicity examined by an animal experimentbeforehand and the estimated exposure amount in inhalation determinedabove. Namely, it is expressed as:

 inhalation safety coefficient=inhalation non-influential amount[mg/kg/day]/estimated exposure amount in inhalation [mg/kg/day]

(v) Calculation of Estimated Percutaneous Exposure Amount andPercutaneous Safety Coefficient (S9 and S11)

The above-mentioned residual amount forms a curve such as that shown inFIG. 4A, for example. This residual amount curve is integrated, theaccumulated residual amount of the compound during a specific period (t₁to t₂) is determined (see FIG. 4B), and the mean residual amount iscomputed from thus determined value. While an arbitrary period is set asthe specific period depending on the object, an appropriate period isusually set in view of the method of use of the product and the testperiod of toxicity data.

Then, according to the mean residual amount, skin attachment ratio,contact area, and body weight, the estimated percutaneous exposureamount is determined. Namely, calculation of:

estimated percutaneous exposure amount [mg/kg/day]=(mean residual amount[mg/m²]×skin attachment ratio [%]×contact area [m²/day])/body weight[kg]

is effected. Here, as the contact area, a published value (e.g., 4[m²/day]) may be used. The skin attachment ratio is a ratio of thecompound attaching to the skin when the latter is in contact with thefloor 5 where the compound exists. As this value, a published value or avalue experimentally obtained from a model may be used.

A model experiment method for the skin attachment ratio is as follows. Aweight (8 cm×8 cm×8 cm; 4.2 kg) is placed on a denim cloth (8 cm×10 cm)with a pressure similar to that of an infant in contact with a floor,and the denim cloth is pulled on the floor at a speed (120 cm/15 sec)similar to the moving speed of the infant. The denim and floor areanalyzed so as to compute the compound contained in the denim and floor.From the ratio therebetween, the skin attachment ratio is obtained. Ithas been confirmed that the skin attachment ratio obtained by thismethod is identical to or slightly higher than that determined fromanalyzed values of a hand and a floor when the hand is actually pressedagainst the floor, thereby proving this model experiment method to beuseful for evaluating exposure of inhabitants.

The percutaneous safety coefficient is computed from the non-influentialamount concerning percutaneous toxicity examined by an animal experimentbeforehand and the estimated percutaneous exposure amount determinedabove. Namely, it is expressed as:

percutaneous safety coefficient=percutaneous non-influential amount[mg/kg/day]/estimated percutaneous exposure amount [mg/kg/day]

Nevertheless, in general, percutaneous non-influential amount has notoften been determined, and there are not many published values.Accordingly, a more accurate value can be determined from the estimatedpercutaneous exposure amount, and oral non-influential amount andpercutaneous absorption ratio for which many published values exist,according to the following expression:

percutaneous safety coefficient=oral non-influential amount[mg/kg/day]/(estimated percutaneous exposure amount[mg/kg/day]×percutaneous absorption ratio [%])

Here, when the percutaneous absorption ratio is unknown, employed is anational guideline (e.g., 10%) which usually exists.

(vi) Calculation of Estimated Oral Exposure Amount and Oral SafetyCoefficient (S13 and S14)

From the estimated percutaneous exposure amount obtained in theabove-mentioned item (v), hand surface area ratio, and oral transferenceratio, the estimated oral exposure amount from hand to mouth isdetermined. Namely, calculation of:

estimated oral exposure amount [mg/kg/day]=estimated percutaneousexposure amount [mg/kg/day]×hand surface area ratio [%]×oraltransference ratio [%]

is effected. Here, the hand surface area ratio is expressed by (handsurface area/body surface area), for which a published value (e.g.,5[%]) may be used. The oral transference ratio is a hypothetical value,which is set to 100%, for example.

In the case where oral exposure might occur via tableware or foodcontaminated with the residually sprayed compound, it is required thatthe estimated oral exposure amount from tableware or food to mouth beadded to the estimated oral exposure amount from hand to mouth to yieldthe total estimated oral exposure amount. For example, the estimatedoral exposure amount from tableware is obtained when, according to thetableware residual amount indicating the amount of the harmful materialremaining in tableware, tableware use area which is the sum of tablewaresurface areas, and oral transference ratio from tableware, calculationof:

estimated oral exposure amount [mg/kg/day]=tableware residual amount[mg/m²]×tableware use area [m²/day]×oral transference ratio [%]/bodyweight [kg]

is effected. Here, the tableware residual amount is expressed by (meanfloor residual amount×tableware contamination ratio). As the tablewarecontamination ratio, an actually measured value (e.g., 9%) or ahypothetical value may be used.

The oral safety coefficient is computed from the non-influential amountconcerning oral toxicity examined by an animal experiment beforehand andthe estimated oral exposure amount determined above. Namely, it isexpressed as:

 oral safety coefficient=oral non-influential amount[mg/kg/day]/estimated oral exposure amount [mg/kg/day]

As mentioned in the foregoing, in the method of estimating an indoorbehavior of a pesticidal compound in this embodiment, the environment isinitially divided into the spraying site 1, large and small particles 2and 3, whole indoor air 4, floor 5, wall 6, and ceiling 7; anddifferential equations concerning Fugacity of the compound in them aresimultaneously formed and are solved, so as to estimate the indoorbehavior of the compound when a chemical containing the compound isresidually sprayed.

Since the environment is thus considered to be seven kinds of media, andexchanges between the individual media and the like are taken intoaccount, simulation results close to the actual behavior of the compoundcan be obtained.

The estimation nick time width set when solving the simultaneousdifferential equations is variably set, while constantly confirming massbalance of the compound indoors after the residual spraying, so that theamount of input of the chemical indoors and the resulting solutioncoincide with each other.

Accordingly, since mass balance of the compound after the residualspraying is always monitored such that the amount of input of thecompound indoors and the resulting solution coincide with each other,thereby varying the estimation nick time width; the estimation nick timewidth is set longer when the mass balance fluctuates a little, whereasit is set shorter when the mass balance starts fluctuating greatly.Namely, when solving simultaneous differential equations including aparameter accompanying temporal change, the estimation nick time widthis automatically set in response to the fluctuation in mass balance.Consequently, when processed by a computer, an accurate solution can beobtained in a short time.

The method of evaluating safety of a pesticidal compound in accordancewith this embodiment uses the estimated result mentioned above toevaluate the safety of the compound with respect to the human body whenthe chemical is residually sprayed.

Accordingly, the safety of the compound with respect to the human bodycan be evaluated accurately in a short time. As a consequence, whenformulating a chemical such as insecticide containing the compound,simulation can be easily repeated while changing conditions, therebymaking it easier to formulate a chemical having a high safety conformingto the aimed object.

Though the kind of the floor 5 is assumed to be flooring in thisembodiment, differential equations similar to those mentioned above mayalso be formed in the case of tatami. In this case, however, whendetermining fugacity capacity (Z₅) of the floor 5 in equation (5), it isnecessary for the particle-constituting solvent component content (seeTable 3) to be changed from that of the flooring to that of tatami.Also, when determining the degradation constant (K₅) of the floor 5 inequation (6), the decomposition half-life is required to be changed fromthat of the flooring to that of tatami.

Though Fugacity is determined by use of Runge-Kutta-Gill method in thisembodiment, other methods may be used for solving differentialequations. Runge-Kutta-Gill method, however, is preferably used since aprogram for the above-mentioned differential equations can be easilymade by Basic. Also in the case where differential equations are solvedby a method other than Runge-Kutta-Gill method, similar effects can beobtained when the estimation nick time width is set as mentioned above.

In the following, examples (Examples 1 to 5) of the above-mentionedmethod of estimating an indoor behavior of a pesticidal compound and thesafety evaluation method using the same will be explained with referenceto the accompanying drawings.

The evaluation of the method of estimating an indoor behavior of apesticidal compound in these examples is effected as the resultsobtained by estimation and the actually measured values obtained bymeasurement of the actual indoor behavior of the compound are comparedwith each other.

First, the measurement of the actual indoor behavior of the compoundwill be explained.

The employed aerosol can (300 [ml]) contains 0.9 [g] of d-phenothrin(trademark: Smithrin; C₂₃H₂₆O₃:(3-phenoxyphenyl)methyl(1R)-cis-trans-2,2-dimethyl-3-(2-methyl-1-prophenyl)cyclopropanecarboxylate) and 1.1 [g] of d-tetramethrin (trademark: Neo-PyraminForte; C₁₉H₂₅O₄:(1,3,4,5,6,7-hexahydro-1,3-dioxo-2H-isoindol-2-yl)methyl(1R)-cis-trans-2,2-dimethyl-3-(2-methyl-1-prophenyl)cyclopropanecarboxylate).

The indoor environment is assumed to be a six-mat room (9.72 [m²]) of atypical apartment in Japan. In conformity to the description of theabove-mentioned aerosol can, spraying was effected at a rate of 60[sec/m²] from a distance of about 20 [cm] from the floor and wall. Thespraying site had a width of 10 [cm] or 15 [cm] from the boundarybetween the floor and the wall toward the floor, and a width of 10 [cm]or 15 [cm] from the boundary toward the wall [see FIG. 2]. The totalspraying period was 2.5 minutes for 2.52 [m²] in the region having awidth of 10 [cm], and 3.7 minutes for 3.78 [m²] in the region having awidth of 15 [cm].

Five kinds of measurement were effected while the room conditions werechanged as shown in Table 7. Namely, measurement in the case withcontinuous use (Example 1), case with changing ventilation rate (Example2), case with an open window (Example 3), and case with air-conditioneron (Example 4), and measurement for skin attachment ratio (Example 5)were performed.

TABLE 7 EXAMPLE 1 EXAMPLE 2 EXAMPLE 3 EXAMPLE 4 EXAMPLE 5 MEASUREMENTSITE AIR, FLOOR, WALL, AIR AIR AIR FLOOR, HAND, CEILING DENIM CLOTHSPRAYING PERIOD [min/day] 2.5 min/2 week × 4   3.7   2.5   2.5   2.5AIR - CONDITIONER STATE OFF OFF OFF ON OFF ROOM TEMP [° C.] 25 25 25 2525 HUMIDITY [% RH] 60 50 60 60 62 WINDOW STATE CLOSED CLOSED 5 min -OPEN CLOSED CLOSED OR 2 h - OPEN ILLUMINATION CONDITION SYNTHETIC LIGHTNONE BASICALLY NONE NONE NONE AND NATURAL LIGHT  0  0  0 ILLUMINANCE[lux] 1320 VENTILATION RATE [h^(−1])    1.58 0.50 OR 1.5 g 1.86, 10.6   1.56    1.54 OR 4.14

In Example 1, spraying was effected four times at a rate of once in twoweeks. The air-conditioner was not actuated, and the windows of the roomwere closed. The room temperature and humidity were controlled so as tobecome 25[° C.] and 60[%], respectively. The illumination condition wassuch that synthetic light illuminates indoors from 7 a.m. to 10 a.m. andfrom 6 p.m. to 11 p.m., while natural light was provided through twowindows. The ventilation rate was set to 1.5 [h⁻¹], which was minimallynecessary for a Japanese woman and an infant to inhabit. Thetemperature, humidity, illuminance, and ventilation rate of the roomactually measured under such a condition are shown in Table 7, eachbeing represented by the mean value in measurement. The temperature,humidity, and illuminance are measured at the center of the room. Theventilation rate was confirmed before and after the measurement.

In Example 2, the illumination condition was in the dark as naturallight was cut. For performing measurement, the ventilation rate waschanged to 0.5 to 4 [h⁻¹] since the actual ventilation rate of Japaneseapartment with closed windows is 0.5 to 3 [h⁻¹].

In Example 3, immediately after spraying, a window was opened for 5minutes or 2 hours in conformity to the description of the aerosol can.While the illumination condition was basically in the dark (illuminance0 [lux] in Table 7), natural light entered when the window was open(mean illuminance 1890 [lux] in Table 7).

The sampling processing in each of the above-mentioned measurements waseffected as follows.

In Examples 1 to 4, the indoor air was sampled after a specified periodfrom the spraying. Here, as for d-phenothrin and d-tetramethrin, at thepositions corresponding to the respiration regions of an infant and anadult, air suction amount was adjusted such that particles having adiameter of 30 [μm] or less can be collected, whereby not only thecompounds in a gas state but also those in a suspended particle statewere sampled.

In Example 1, at the centers of floor, wall, and ceiling, strips ofmaterials identical thereto each having a size of 5 [cm]×5 [cm] wereplaced before spraying, whereby sampling was effected at the floor,wall, and ceiling. As for the wall, sampling was effected at threeplaces consisting of the inflow and discharge sides of the air and alateral side apart therefrom.

In the collecting tube that had sampled the air, flooring strip,wallpaper strip, ceiling strip, hand, and denim cloth, d-phenothrin andd-tetramethrin were analyzed by the methods shown in Table 8. In thesemethods, an organic solvent containing BHT (2,6-di-t-butyl-p-cresol) wasused to extract these compounds, and cleanup was effected whennecessary, so that analysis was effected by mass spectrometer (MSD)attached to a gas chromatography (GC). In each process, in order toprevent the compound from vaporizing due to evaporation of the solvent,diethylene glycol or octanol is added. Both d-phenothrin (mass: 183[m/z]) and d-tetramethrin (mass: 164 [m/z]) were detected in 9 minutesunder the GC condition noted in the following. As the apparatus,Shimadzu GC-MS QP-1100EX (Mode EI, 70 ev) was used with a DC-608 column(inner diameter: 0.53 [mm], length: 30 [m], thickness; 0.8 [μm])programmed to raise temperature at a rate of 10[° C./min] from 205[°C.], whereas the temperature of injection and ion source was 260[° C.].

TABLE 8 CLEANUP RECOVERY [%] MEDIUM EXTRACT d-phenothrin d-tetramethrind-phenothrin d-tetramethrin DETECTION LIMIT COLLECTING HEXANE/ NONE NONE103 107 0.05 [μg/m³] TUBE ACETONE MBE-FL FLOOR DICHLOROMETANE FL 92.778.3   8 [μg/m²] WALL HEXANE GPC 93.2 89.8   8 [μg/m²] MBE-FL CEILINGMBE-FL HAND 2- MBE-NH₂ SI 87.7 92.8 0.05 [μg/hand] PROPANOL MBE-SI DENIMCLOTH HEXANE MBE-FL 92.8 103   8 [μg/m²] NOTE) MBE:MEGABOND ELUTE,FL:FLORISIL, SI:SILICA GELL, GPC:GELL PERMEATION COLUMN.

The results of concentrations of d-phenothrin and d-tetramethrin in theair and the residual amounts in the floor, wall, and ceiling measured bythe above-mentioned methods will be explained.

In Example 1, the concentration in the air was measured for 125 daysincluding the time in which spraying was effected once (2.5 minutes) per2 weeks for 8 weeks. As shown in FIG. 7, the concentration in the airexhibited its maximum level immediately after spraying, where theaverage of d-phenothrin at the heights of 25 [cm] and 120 [cm] from thecenter of the floor was 752 [μg/m³] and that of d-tetramethrin was 1040[μg/m³], and rapidly decreased thereafter. Here, since the half-life ofeach of both compounds was short, i.e., about 20 minutes, there were 4peaks in the 8 weeks of spraying period. The concentration in the airafter the spraying period was less than 0.10 [μg/m³] in both of them.Further, there was no substantial difference in concentration betweenthe heights of 25 [cm] and 120 [cm] from the floor. Also, no increasewas seen in the concentration in the air due to the increase in thenumber of spraying operations. In FIG. 7, concentrations which were lessthan the detection limit (0.05 [μg/m³]) and thus could not be measuredare plotted at the detection limit.

The total spraying amount was 250 [g], including 1.11 [g] ofd-phenothrin and 1.38 [μg] of d-tetramethrin, which equal 1.2 aerosolcans of 300 [ml]. Since 5 million aerosol cans of 300 [ml] for residualspraying are annually sold in Japan, annual consumption per household iscalculated as 0.13 can. Accordingly, it is seen that the spraying amountused for measurement (1.3 cans per room) is considerably greater thanthe actual annual consumption.

As shown in Table 9, the mean concentration in the air during thespraying period and the mean annual concentration in the air including8-week spraying period were calculated as 2.35 [μg/m³]/0.43 [μg/m³] ford-phenothrin, and 3.25 [μg/m³]/0.53 [μg/m³] for d-tetramethrin.Consequently, it is seen that the amount of existence of d-phenothrinwith respect to d-tetramethrin in the air corresponds to their ratio ofexistence within the aerosol can. In Table 9, for those less than thedetection limit value, the mean concentration in the air was calculatedby use of the detection limit value.

TABLE 9 CONCENTRATION IN AIR [μg/m³] RESIDUAL AMOUNT [μg/m²] COMPOUNDPERIOD 25 [cm] 120 [cm] FLOOR WALL CEILING d-phenothrin SPRAYING PERIOD2.35 2.35 2200 33 27 ANNUAL 0.41 0.45 360 7 9 d-tetramethrin SPRAYINGPERIOD 3.31 3.19 2500 43 34 ANNUAL 0.54 0.52 400 15 30

In Example 2, concentrations of d-phenothrin and d-tetramethrin in theair after 3.7 minutes from the spraying with changed ventilation ratiowere measured. FIG. 8A shows only the results of d-phenothrin. This hasindicated that the half-lives in the air at ventilation ratios of 1.58[h⁻¹], 0.50 [h⁻¹], and 4.14 [h⁻¹] are 21 minutes, 58 minutes, and 11minutes, respectively.

In Example 3, immediately after the chemical was sprayed for 2.5minutes, the window was opened, and the concentrations of d-phenothrinand d-tetramethrin in the air were measured. FIG. 8B shows the resultsof d-phenothrin. This has indicated that the half-lives in the caseswhere the window was opened for 5 minutes, the window was opened for 2hours, and the window was kept closed are 14 minutes, 4 minutes, and 20minutes, respectively. Also, the mean concentration (2.88 [μg/m³] whenopened for 5 minutes, 1.19 [μg/m³] when opened for 2 hours) was lessthan ⅕ that of the closed state (14.8 [μg/m³]).

The measured values of FIGS. 8A and 8B are mean values of theconcentrations in the air respectively sampled at heights of 25 [cm] and120 [cm] from the floor. Also, for those less than the detection limitand thereby incapable of measurement were plotted as the detection limitvalue (0.05 [μg/m³]).

Table 10 lists the above-mentioned half-lives. These results haveindicated that, in the residual spraying, the ventilation of room,opening the window immediately after spraying in particular, is highlyinfluential in the concentration in the air. For reference, Table 10shows half-lives of compounds (d-resmethrin and d-tetramethrin) in theair when a chemical is sprayed in the space.

TABLE 10 VENTILATION HALF - LIFE OF RESIDUAL HALF - LIFE OF SPATIAL RATEOR SPRAYING [min] SPRAYING [min] MEASUREMENT WINDOW STATE d-phenothrind-tetramethrin d-resmethrin d-tetramethrin EXAMPLE 1 1.58 [h⁻¹] 20 20 1623 EXAMPLE 2 0.50 [h⁻¹] 58 58 — 49 1.58 [h⁻¹] 21 22 — 19 4.14 [h⁻¹] 1111 — 8 EXAMPLE 3 5 min OPEN 14 14 9 12 2 h OPEN 4 4 4 3

Meanwhile, in the state where the window is open as with Example 3, forexample, the half-lives caused by photodegradation are estimatedaccording to the above-mentioned Atmospheric Oxidation program from thestructures of compounds to be 2.1 hours for d-phenothrin and 1.7 hoursfor d-tetramethrin. Since the half-lives in the air are shorter than thehalf-lives caused by photodegradation, the decreases in concentration ofd-phenothrin and d-tetramethrin are considered to be mainly caused byventilation rather than photodegradation.

In Example 4, the mean concentration when the air-conditioner was used(11.6 [μg/m³] for d-phenothrin, 15.5 [μg/m³] for d-tetramethrin) wassubstantially the same as the mean concentration when theair-conditioner was not used (14.8 [μg/m³] for d-phenothrin, 20.2[/μg/m³] for d-tetramethrin). This has indicated that the influence ofthe air convection and absorption of the air into the filter of the airconditioner upon the concentration in the air is substantiallynegligible.

FIGS. 9A and 9B and the above-mentioned Table 9 show the results ofmeasurement of residual amounts at the floor, wall, and ceiling for 125days in Example 1. The values of the residual amounts at the wall inFIG. 9B and Table 9 are means of values on the air inflow and dischargesides and their lateral side, whereas the residual amounts of wall andceiling in FIG. 9B are plotted as the mean values of residual amounts atthe wall and ceiling.

As the air flows in and out, the residual amount at the wall on theinflow side (28 [μg/m²] for d-phenothrin, 35 [μg/m²] for d-tetramethrin)was less than the residual amount at the wall on the discharge side orlateral side (45 [μg/m²] and 58 [μg/m²] on the discharge side, 33[μg/m²] and 43 [μg/m²] on the lateral side). Also, while the residualamounts of d-phenothrin and d-tetramethrin enhanced as the number ofspraying operations increased, they gradually decreased after spraying.Here, half-lives of d-phenothrin and d-tetramethrin at the floor wererespectively 13 days and 20 days, whereas their half-lives at thewall/ceiling were respectively 31 to 41 days and 24 to 75 days. Thesevalues are longer than those in the air, since the materials of floor,wall, and ceiling contain a large amount of antioxidants. Also, theresidual amount at the floor, except for the site sprayed with thechemical, is greater than the residual amount at the wall or ceiling,since the suspended particles attach to the floor.

In Example 5, a hand attachment test in which a hand is directly pressedagainst the floor where the compound remains, and a wiping test using adenim cloth instead of the hand are performed, so as to measure the skinattachment ratios of d-phenothrin and d-tetramethrin at the flooring.When Student's t-test (P≦0.05) was performed, the skin attachment ratiosobtained by the wiping test (0.31[%] and 0.33[%] respectively ford-phenothrin and d-tetramethrin after 6 hours from spraying, 0.17[%] and0.09[%] after 24 hours from spraying) were equal to or higher than theresults obtained by the hand attachment test (0.22[%] and 0.32[%]respectively for d-phenothrin and d-tetramethrin after 6 hours fromspraying, 0.06[%] and 0.07[%] after 24 hours from spraying). This hasindicated that the safety of percutaneous exposure can be sufficientlyestimated when the skin attachment ratio is determined by the wipingtest alone.

In the following, simulation results obtained according to the method ofestimating an indoor behavior of a compound in accordance with thepresent invention will be explained. The condition here is the same asthat of the above-mentioned Example 1. As the primary condition, thevalues described in Tables 1 to 4 of the first embodiment were inputted.

When the behavior of d-phenothrin caused by residual spraying during theperiod after 2.5 minutes to 24 hours from the spraying was simulated,the results shown in Table 11 were obtained. In the table, “suspensionperiod” refers to a period in which the particles floating at theposition lower than 2.4 [m] fall onto the floor or disappear in the air,whereas “transference amount” refers to the ratio of compound amounttransferred within 24 hours with respect to the whole spraying amount.

TABLE 11 BEHAVIOR FROM TO RATIO CHANGE IN DIAMETER OF LARGE PARTICLES 20[μM] 3.6 [μm] (CHANGE IN 35 sec.) SMALL PARTICLES  5 [μM] 0.9 [μm](CHANGE IN 2.2 sec.) SUSPENSION PERIOD OF LARGE PARTICLES  0 [h] 2.0 [h]SMALL PARTICLES  0 [h]  30 [h] TRANSFERENCE AMOUNT AIR (WITH PARTICLE)SPRAYING SITE 1.0 [%] AIR (WITH PARTICLE) FLOOR 7.0 [%] AIR (WITHPARTICLE) WALL 0.44 [%] AIR (WITH PARTICLE) CEILING 0.10 [%] SPRAYINGSITE AIR 0.16 [%] FLOOR AIR 0.15 [%] WALL AIR 0.0011 [%] CEILING AIR0.00023 [%] VENTILATION AMOUNT INDOOR OUTDOOR 29 [%] DEGRADATION AMOUNTIN SPRAYING SITE 1.7 [%] AIR (WITH PARTICLES) 3.2 [%] FLOOR 0.35 [%]WALL 0.0080 [%] CEILING 0.0018 [%] RESIDUAL AMOUNT IN SPRAYING SITE 58[%] AIR (WITH PARTICLES) 0.00060 [%] FLOOR 6.5 [%] WALL 0.42 [%] CEILING0.10 [%]

According to these results, the main solvent in the large particles(diameter: 20 [μm]) was completely evaporated after 35 seconds, anddisappeared from within the air after 2 hours. The main solvent in thesmall particles (diameter: 5 [μm]) was completely evaporated after 2.2seconds, and existed in the air for 30 hours. The chemical containingthe particles in the air (40[%] of the amount of chemical immediatelyafter spraying) was distributed to the spraying site by 1.0[%], floor by7.0[%], wall by 0.44[%], and ceiling by 0.10[%], whereas the remaining29[%] went outdoors, and 3.2[%] was degraded in the air. Of the chemicalat the spraying site (60[%] of the amount of chemical immediately afterspraying), 0.16[%] of the sprayed amount was evaporated into the airwithin 24 hours, 1.7[%] was degraded by light or oxidation, and theremaining 58[%] was left at the spraying site.

When the simulation results concerning the concentration in the air andthe residual amounts at the spraying site and floor/wall/ceiling and theactually measured values which is mentioned above were compared witheach other, relationships shown in FIGS. 10A and 10B were obtained. Inthese graphs, solid lines show simulation results, whereas plottedpoints indicate actually measured values. These actually measured valueswere derived from the results of Example 1.

From these graphs, it can be seen that the estimated results accordingto the method of estimating an indoor behavior of a compound inaccordance with the present invention are very close to the actuallymeasured values. Namely, upon residual spraying, the most part of thechemical in the air is discharged outdoors or falls onto the floor. Thechemical at the spraying site permeated through the floor or wall, andwas slightly degraded or evaporated.

In the following, the results obtained according to the method ofevaluating safety of a compound in accordance with the present inventionwill be explained. Here, indoor exposure amounts of d-phenothrin andd-tetramethrin with respect to inhabitants including an infant when achemical was residually sprayed at the boundary between the floor andwall for four times in eight weeks (sprayed for 2.5 minutes for eachtime) were evaluated.

The inhabitants inhale vapors or particles of d-phenothrin andd-tetramethrin existing in the air. Since humans inhale aerosolparticles having a diameter not greater than 8 [μm] to the lungs,sampling the particles having a size not greater than 30 [μm] and vaporchemicals is sufficient for evaluating the exposure in inhalation.

The following Table 12 shows the estimated exposure amount in inhalationcalculated by use of the mean indoor concentration in the air (see“spraying period” in Table 9), respiration amount, and exposure time asexplained in item (iv) in the first embodiment. Here, the mean indoorrespiration amount of Japanese is 0.220 [L/min/kg] for an adult, and0.235 [L/min/kg] for an infant. Also, the exposure time was presumed tobe 24 [h/day], taking account of the worst case where inhabitants areconfined in the room for 24 hours after spraying.

TABLE 12 INHALA- INHALA- TION TION PER- COM- (WINDOW (WINDOW CUTA- POUNDSUBJECT CLOSED) OPEN) NEOUS ORAL d-phenothrin INFANT 0.795 0.159 2.710.135 ADULT 0.744 0.149 0.553 — d- INFANT 1.12 0.224 2.15 0.107tetramethrin ADULT 1.01 0.202 0.438 —

In the table, “window closed” refers to the case where the window isclosed throughout the exposure time, whereas “window open” refers to thecase where spraying was effected in the state with the closed window andthen the window was opened for 5 minutes (Example 3).

Also, Table 12 shows the estimated percutaneous exposure amountcalculated by use of the mean floor residual amount (see “sprayingperiod” in Table 9), skin attachment ratio, contact area, and bodyweight as explained in item (v) in the first embodiment. Here, it wasassumed that the contact area for an infant and an adult was 4.0[m²/day], the body weight of the infant was 10.2 [kg], and the bodyweight of the adult was 50 [kg]. As the skin attachment ratios ford-phenothrin and d-tetramethrin at the flooring, values evaluated byintegration and extrapolation of the measured values in Example 5 wereused. Namely, the skin attachment ratio was 0.31[%] for d-phenothrin,and 0.25[%] for d-tetramethrin. These values were used for calculatingthe estimated percutaneous exposure amount.

Further, Table 12 shows the estimated oral exposure amount calculated byuse of the estimated percutaneous exposure amount, hand surface arearatio, and oral transference ratio as explained in item (vi) in thefirst embodiment. Here, while the hand surface area ratio was assumed tobe about 5[%], and the oral transference ratio was presumed to be theworst case of 100[%], only the estimated oral exposure amount of theinfant was calculated.

Table 13 lists the inhalation safety coefficient, percutaneous safetycoefficient, and oral safety coefficient obtained according to theestimated exposure amount in inhalation, estimated percutaneous exposureamount, and estimated oral exposure amount determined by theabove-mentioned calculations. At the same time, the total safetycoefficient determined from the above-mentioned three safetycoefficients are shown in the table. Further shown in the table is thesafety coefficient with respect to both of d-phenothrin andd-tetramethrin computed when the sum of the respective reciprocals ofthe safety coefficient (inhalation, percutaneous, or oral) ofd-phenothrin and the safety coefficient (inhalation, percutaneous, ororal) of d-tetramethrin is determined and then is turned into thereciprocal.

TABLE 13 SUBJECT INHALATION INHALATION TOTAL TOTAL COMPOUND (WINDOWCLOSED) (WINDOW OPEN) PERCUTANEOUS ORAL (WINDOW CLOSED) (WINDOW OPEN)d-phenothrin INFANT 23,100 116,000 369,000 923,000 21,300 80,400 ADULT24,700 124,000 1,810,000 — 24,400 116,000 d-tetramethrin INFANT 2,88014,400 465,000 100,000 2,780 12,200 ADULT 3,190 15,900 2,280,000 — 3,18015,800 BOTH INFANT 2,560 12,800 206,000 90,300 2,460 10,600 ADULT 2,82014,100 1,010,000 — 2,820 13,900

Here, the non-influential amount of a rat concerning d-phenothrin was18.4 [mg/kg/day] (=non-influential in-air concentration 210 [mg/m³]×ratrespiration amount 0.365 [L/min/kg]×rat exposure time 4 [h/day]; 4-weektest with exposure of 6 days a week) in inhalation, 1000 [mg/kg/day](21-day test) for percutaneous exposure, and 125 [mg/kg/day] (6-monthtest) for oral exposure. On the other hand, the non-influential amountof a rat concerning d-tetramethrin was 3.22 [mg/kg/day](=non-influential in-air concentration 49 [mg/m³]×rat respiration amount0.365 [L/min/kg]×rat exposure time 3 [h/day]; 4-week test with exposureof 7 days a week) in inhalation, 1000 [mg/kg/day] (21-day test) forpercutaneous exposure, and 10.75 [mg/kg/day] (6-month test) for oralexposure.

As a result, it has been confirmed that the safety coefficient of theinfant is lower than that of the adult, and that the safety coefficientsof d-phenothrin were higher than the safety coefficients ofd-tetramethrin except for the percutaneous safety coefficient. Also,since the inhalation safety coefficient is the lowest of the three, itsubstantially determines the value of total safety coefficient whenexposed by all of the three kinds of exposure routes.

(2) Second Embodiment

With reference to the drawings, the second embodiment of the presentinvention will be explained in the following. The method of simulatingan indoor behavior of a pesticidal compound in accordance with thisembodiment estimates the behavior of the compound in the case where thefloor in the first embodiment is constituted by a rug having ears offiber. For convenience of explanation, members identical to those shownin the drawings of the previous embodiment will be referred to withnumerals or letters identical thereto, without their explanationsprovided. Explained here is a case where only the kind of floor at thespraying site is a carpet (e.g., the floor spraying region indicated byc in FIG. 2 is assumed to be a carpet), whereas the other part of thefloor is treated as a mere plane. Accordingly, only the portiondifferent from the first embodiment will be explained.

Here, though the kind of floor (whole surface) may be a carpet, only thesuspended particles fall onto the floor other than the spraying site,whereby the behavior of the floor does not greatly differ from that inthe case of flooring. Accordingly, it is often only necessary forFugacity capacity of the floor to be corrected with theparticle-constituting solvent component content alone.

First, the carpet is modeled as shown in FIGS. 6A, 6B, and 6C. Namely,the carpet is divided into a plurality of carpet fibers (ears of fiber)planted on a substrate, and space portions existing between the fibers.When a chemical is residually sprayed in a room in which such a carpetcovers the whole floor surface, the chemical infiltrates into the carpetfiber at the spraying site, and accumulates in the space portion.

While the method of simulating an indoor behavior of a pesticidalcompound in accordance with this embodiment also conforms to theflowchart of FIG. 1, at S1, as the primary condition, the carpet-relatedprimary condition shown in Table 14 is added to the primary condition ofthe first embodiment (see Tables 1 to 4). Here, the cross-sectional area(A_(c)) of the space portion of the carpet refers to the area in whichthe space portion is in contact with the indoor air (see FIGS. 6A, 6B,and 6C).

TABLE 14 CARPET - RELATED PRIMARY CONDITION SYMBOL EXAMPLE OF VALUECARPET CROSS - SECTIONAL AREA A_(c) 1.6 × 10⁻³ [m²/m² FLOOR] OF SPACEPORTION OF CARPET AREA IN WHICH CARPET A_(c1) 0.192 [m²/m² FLOOR] FIBERIS IN CONTACT WITH COMPOUND IN SPACE PORTION AREA IN WHICH CARPET A_(a1)1.19 [m²/m² FLOOR] FIBER IS IN CONTACT WITH COMPOUND PRODUCT PROPERTYCONTENT OF SOLVENT C_(sd) (XYLENE) CONTAINED IN PRODUCT DILUTION OFPRODUCT X_(sol)

The examples of values in Table 14 are based on the values shown inFIGS. 6A, 6B, and 6C. Here, one space portion is set to a size of 0.1[mm]×0.1 [mm]×3 [mm], and one square of carpet fiber is set to a size of2.5 [mm]×2.5 [mm]×3 [mm]. Also, it is assumed that 16 [pieces] of carpetfiber exist in 1 [cm²].

In this case, the individual parameters can be determined as:$\begin{matrix}{A_{c} = {\left( {{0.1\quad\lbrack{mm}\rbrack} \times {0.1\quad\lbrack{mm}\rbrack} \times {16\quad\lbrack{pieces}\rbrack}} \right)\text{/}{1\quad\lbrack{cm}\rbrack}}} \\{= {1.6 \times {10^{- 3}\quad\left\lbrack {m^{2}\text{/}m^{2}\quad {floor}} \right\rbrack}}} \\{A_{c1} = {\left( {{0.1\quad\lbrack{mm}\rbrack} \times {3\quad\lbrack{mm}\rbrack} \times {4\quad\lbrack{faces}\rbrack} \times {16\quad\lbrack{pieces}\rbrack}} \right)\text{/}{1\quad\lbrack{cm}\rbrack}}} \\{= {0.192\quad\left\lbrack {m^{2}\text{/}m^{2}\quad {floor}} \right\rbrack}} \\{A_{1} = {1 - A_{c}}} \\{= {1 - {1.6 \times {10^{- 3}\quad\left\lbrack {m^{2}\text{/}m^{2}\quad {floor}} \right\rbrack}}}} \\{A_{a1} = {A_{1} + A_{c1}}} \\{= {1.19\quad\left\lbrack {m^{2}\text{/}m^{2}\quad {floor}} \right\rbrack}}\end{matrix}$

Here, A₁, which is the area occupied by the spraying site in the firstembodiment, is replaced by the area in which the carpet fibers in 1 [m²]are in contact with the indoor air.

As the secondary condition at S2, the carpet-related secondary conditionshown in Table 15 is added to the secondary condition of the firstembodiment. Here, k₁ and V₁, which are respectively transference speedof the compound in the spraying site and the volume of the spraying sitein the first embodiment (see Table 6), are respectively replaced by thetransference speed of the compound in the carpet fiber and the volume ofthe whole fiber of the carpet.

TABLE 15 CARPET - RELATED SECONDARY CONDITION SYMBOL DEFINITE FACTORCONDITION EVAPORATION CONSTANT OF CHEMICAL IN SPACE R_(d) PORTIONHUMIDITY AT TEMPERATURE (T_(d)) OF SPACE H_(m) PORTION VOLUME OF WHOLEFIBER OF CARPET V₁ TRANSFERENCE SPEED OF COMPOUND IN PRODUCT k_(c)PROPERTY CHANGE CONSTANT OF PRODUCT a TEMPORAL CHANGE CONDITIONTRANSFERENCE COEFFICIENT OF COMPOUND D_(c4) BETWEEN CHEMICAL IN SPACEPORTION AND AIR TRANSFERENCE COEFFICIENT OF COMPOUND D_(c1) BETWEENCHEMICAL IN SPACE PORTION AND CARPET FIBER VOLUME OF CHEMICAL IN SPACEPORTION V_(c) FUGACITY CAPACITY OF CHEMICAL IN SPACE Z_(c) PORTION

A method of computing the definite factor conditions and temporal changeconditions shown in the above-mentioned Table 15 will be explainedhereinafter as exemplified by the case using an aqueous aerosol, i.e.,case where the particle-constituting solvent is water.

From the cross-sectional area (A_(c)) of the space portion, roomtemperature (T), and humidity (H), the evaporation constant (R_(d)) ofthe chemical entered into the space portion of the carpet is expressedas: $\begin{matrix}\left. \begin{matrix}{R_{d} = {A_{c}{{h\left( {H_{m} - H} \right)}/C_{H}}}} \\{C_{H} = {0.24 + {0.46H}}} \\{h = {3.06 \times 10^{- 4}\left( {T - T_{d}} \right)^{1/3}}}\end{matrix} \right\} & (20)\end{matrix}$

wherein T_(d) is the temperature of the space portion of the carpet(corresponding to the wet-bulb temperature), and H_(m) is the humidity(corresponding to the saturated humidity at the wet-bulb temperature) ofthe space portion at T_(d). Here, T_(d) and H_(m) can be determined fromthe above-mentioned “mass-based humidity table” according to the roomtemperature (T) and humidity (H). In the case of an oil-based product(aerosol), while the vapor constant of the chemical can be computed whenproperties of the water and oil are compared with each other and thenare multiplied by R_(d), R_(d)=0 may be assumed in the case where theevaporation of the oil is slow. The chemical entered into the spaceportion of the carpet reduces its volume upon evaporation and finallydisappears, leaving the compound. Thus left compound permeates throughthe carpet fiber.

From the diffusion coefficient (D_(c)) in the floor/wall/ceiling and thearea (A_(a1)) in which the carpet fiber is in contact with the compound,the volume (V₁) of the whole fiber of the carpet is determined asfollows:

V ₁=2{square root over (D_(c)/t)} A _(a1) A _(t)  (21)

The transference speed (k_(c)) of the compound in the product isexpressed as k₄/100 by use of k₄ (=GV₄/A₄) which indicates thetransference speed of the compound in the indoor air.

From the above-mentioned transference speed (k_(c)) of the compound inthe product, transference speed (k_(d)) of the compound in the indoorair, area (A_(t)) of the spraying site, cross-sectional area (A_(c)) ofthe space portion, Fugacity capacity (Z_(c)) of the chemical in thespace portion determined by expression (24) which will be mentionedlater, and Fugacity capacity (Z₄) of the air determined by expression(4) of the first embodiment, the transference coefficient (D_(c4)) ofthe compound between the chemical in the space portion of the carpet andthe air is expressed as follows: $\begin{matrix}{D_{c4} = \frac{1}{{1/\left( {k_{c}A_{c}A_{t}Z_{c}} \right)} + {1/\left( {k_{4}A_{c}A_{t}Z_{4}} \right)}}} & (22)\end{matrix}$

From the above-mentioned transference speed (k_(c)) of the compound inthe product, diffusion coefficient (D_(c)), area (A_(t)) of the sprayingsite, area (A_(c1)) in which the carpet fiber is in contact with thecompound in the space portion, Fugacity capacity (Z_(c)) of the chemicalin the space portion, and Fugacity capacity (Z₁) of the floor determinedby expression (2) of the first embodiment, the transference coefficient(D_(c1)) of the compound between the chemical in the space portion andthe carpet fiber is expressed as: $\begin{matrix}{D_{c1} = \frac{1}{{1/\left( {k_{c}A_{c1}A_{t}Z_{c}} \right)} + {1/\left( {k_{1}A_{c1}A_{t}Z_{1}} \right)}}} & (23)\end{matrix}$

wherein the transference speed (k₁) of the compound within the carpetfiber is expressed as (D_(c)/t)^(0.5).

The volume (V_(c)) of the chemical in the space portion is determinedfrom the area (A_(t)) of the spraying site, amount of emission of theparticle-constituting solvent (O_(a)), and evaporation constant (R_(d))of the chemical in the space portion determined by expression (20). Thevolume (V_(c)) of the space portion decreases until the solvent in thechemical completely evaporates.

From the vapor pressure (P^(s)), water solubility (C^(s)), andoctanol/water distribution coefficient (K_(ow)) of the compound, andproperty change constant (a) of the product, Fugacity capacity (Z_(c))of the chemical in the space portion is expressed as:

Z _(c)=(e ^(−at) K _(ow)+1−e ^(−at))C ^(s) /P ^(s)  (24)

Here, the property change constant (a) of the product can be computedaccording to the evaporation constant (R_(d)) of the chemical in thespace portion determined by expression (20), content (C_(sd)) of thesolvent (Xylene) contained in the product, and dilution (X_(sol)) of theproduct. Namely, Fugacity capacity (Z_(c)) of the chemical in the spaceportion is also expressed as:

Z _(o)=[(ratio of organic solvent in product)K_(ow)+(ratio of water inproduct)]×C ^(s) /P ^(s)

By simultaneously forming this expression and the above-mentionedexpression (24), the property change constant (a) of the product iscomputed. Here, in the case of the oil-based product (aerosol), Fugacitycapacity (Z_(c)) of the chemical in the space portion is given byexpression (5) of the first embodiment from the vapor pressure (P^(s)),water solubility (C^(s)), and octanol/water distribution coefficient(K_(ow)) of the compound.

Consequently, the behavior of the compound in the space portion of thecarpet is expressed in the form of differential equation concerningFugacity (f_(c)) as follows: $\begin{matrix}\begin{matrix}{{\frac{f_{c}}{t}V_{c}Z_{c}} = {{\gamma_{1}{\sum\limits_{i = 1}^{3}{n_{i}A_{c}V_{i}Z_{i}f_{i}}}} +}} & {{{Deposition}(i)}} \\{{{R_{d}A_{t}Z_{c}f_{c}} -}} & {{V\text{-}{change}}} \\{{{D_{c1}\left( {f_{c} - f_{1}} \right)} -}} & {{{Transference}(j)}} \\{{{D_{c4}\left( {f_{c} - f_{4}} \right)} -}} & {{{Transference}(5)}} \\{{K_{c}V_{c}Z_{c}f_{c}}} & {{Degradation}}\end{matrix} & (25)\end{matrix}$

Also, expressions (15) and (17) in the first embodiment are respectivelyreplaced by: $\begin{matrix}\begin{matrix}{{\frac{f_{1}}{t}V_{1}Z_{1}} = {{\sqrt{D_{c}/t}A_{c1}A_{t}Z_{1}f_{1}} +}} & {{V\text{-}{change}}} \\{{F\text{-}{change}{\quad }{\sum\limits_{i = 2}^{3}{n_{i}A_{1}A_{t}V_{i}Z_{i}f_{i}}}} -} & {{{Deposition}(i)}} \\{{{D_{c1}\left( {f_{3} - f_{c}} \right)} -}} & {{{Transference}(c)}} \\{{{D_{14}\left( {f_{1} - f_{4}} \right)} -}} & {{{Transference}(1)}} \\{{K_{1}V_{1}Z_{1}{f1}}} & {{Degradation}}\end{matrix} & (26) \\\begin{matrix}{{\frac{f_{4}}{t}V_{4}Z_{4}} = {{{- {GV}_{4}}Z_{4}f_{4}} -}} & {{Ventilation}} \\{{F\text{-}{change}{\quad }{\sum\limits_{i = 2}^{3}{n_{i}{D_{i4}\left( {f_{4} - f_{i}} \right)}}}} -} & {{{Transference}(i)}} \\{{{\sum\limits_{j = 5}^{7}{D_{4j}\left( {f_{4} - f_{j}} \right)}} -}} & {{{Transference}(j)}} \\{{{K_{4}V_{4}Z_{4}f_{4}} -}} & {{Degradation}} \\{{{D_{c4}\left( {f_{4} - f_{c}} \right)} -}} & {{{Transference}(c)}} \\{{D_{14}\left( {f_{4} - f_{1}} \right)}} & {{{Transference}(1)}}\end{matrix} & (27)\end{matrix}$

In expression (26), terms of V-change, Deposition (i), Transference (c),Transference (1), and Degradation respectively indicate the change involume (increase over time) of the carpet fiber, attachment accompanyingthe falling of particles, amount of transference of the compound betweenthe carpet fiber and the space portion, amount of transference of thecompound between the carpet fiber and the air, and change in amount ofphotodegradation of the compound.

In expression (27), terms of Ventilation, Transference (i), Transference(j), Degradation, Transference (c), and Transference (1) respectivelyindicate the amount of discharge of the compound outdoors, amount oftransference of the compound between the air and the particles, amountof transference of the compound between the air and thefloor/ceiling/wall, change in amount of photodegradation of thecompound, amount of transference of the compound between the air and thespace portion at the spraying site, and amount of transference of thecompound between the air and the carpet fiber at the spraying site.

Accordingly, Fugacity calculation at S3 is performed such that eightkinds of differential equations of expressions (16) and (18) in thefirst embodiment and the above-mentioned expressions of (25) to (27) aresolved by Runge-Kutta-Gill method. The subsequent steps of S4 to S17 aresimilar to those in the first embodiment.

As explained in the foregoing, in the method of estimating an indoorbehavior of a pesticidal compound in accordance with this embodiment, inthe case where the kind of the spraying site is a carpet having ears offiber and a space portion between the ears, a differential equation forFugacity in the above-mentioned space portion of the carpet is added toseven kinds of simultaneous differential equations concerning Fugacityof the compound in the spraying site, two kinds of suspended particles,indoor air, floor, wall, and ceiling, so as to calculate each Fugacity.

Consequently, even in the case where the chemical is accumulated in thespace portion, so that the compound behaves differently from the casewith a flat floor, the behavior of the compound can be estimatedaccurately, whereby various kinds of simulations can be performed.

(3) Third Embodiment

With reference to the drawings, the third embodiment of the presentinvention will be explained in the following.

The method of simulating an indoor behavior of a pesticidal compound(hereinafter simply referred to as compound) contained in a chemical(solution) such as insecticide in accordance with this embodiment mainlyestimates the behavior of the compound in the case where the chemical isspatially sprayed in order to terminate indoor vermin such as mosquitoor fly. Here, the chemical encompasses all kinds of insecticidesincluding pyrethroid insecticidal compounds and organophosphorusinsecticidal compounds.

First, as shown in FIG. 11, an environment is classified into sevenkinds of media consisting of large particles (aerosol particles) 2,medium particles (aerosol particles) 8, and small particles (aerosolparticles) 3 having diameters different from each other, whole indoorair 4, floor 5, wall 6, and ceiling 7.

The particles are divided into three kinds since their behavior mainlydepends on their diameter. Though the particles are distributed in thesame site immediately after spraying, as time passes, the largeparticles 2 are distributed into a spraying zone SZ₂ near the floor dueto their weight, the medium particles 8 into a spraying zone SZ₈ in themiddle of the room, and the small particles 3 into a spraying zone SZ₃near the ceiling 7 since they are lighter than the other two kinds ofparticles.

Simultaneous differential equations concerning Fugacity of the compoundin the above-mentioned seven kinds of media are formed and are solved byRunge-Kutta-Gill method, whereby the indoor behavior of the compound inthe chemical when the chemical is sprayed in the indoor space, i.e.,temporal change of compound distribution in the room, is estimated andanalyzed.

Here, since the floor 5 mainly comprises three kinds, i.e., tatami,flooring, and carpet (rug), the differential equation is formed so as tocorrespond to the kind of floor. Explained in this embodiment is thecase where the floor 5 is made of tatami.

With reference to FIG. 1, a method of simulating an indoor behavior ofthe compound will be explained. The simulation method in accordance withthis embodiment can be mainly divided into a step of dividing an indoorenvironment into predetermined media and forming a differential equationconcerning a fugacity of the compound in each medium (S1 to S2); a stepof determining the fugacity of the compound in each medium from thedifferential equation (S3); a step of determining the indoor behavior ofthe compound from the fugacity of the compound in each medium (S4); astep of changing, in response to a fluctuation in mass balance of thecompound indoors, a minute time unit used when solving the differentialequation (S21 to S35, see FIG. 5); and a step of evaluating safety ofthe compound with respect to a human body according to the indoorbehavior of the compound (S5 to S17).

First, at step (herein after abridged as S) 1, a primary condition isinputted. The primary condition comprises physicochemical properties ofthe compound (see Table 16), indoor environmental behavior properties ofthe compound (see Table 17), indoor environment (see Table 18), productproperties (see Table 19), and a spray condition (see Table 20).

TABLE 16 PHYSICOCHEMICAL PROPERTY EXAMPLE OF OF COMPOUND SYMBOL VALUEMOLECULAR WEIGHT — 277.23 [g/mole] SPECIFIC GRAVITY ρ 1.33 × 10⁶ [g/m³]VAPOR PRESSURE P^(S) 2.85 × 10^(−2 [Pa]) WATER SOLUBILITY C^(S) 5.05 ×10^(−2 [mole/m) ³] OCTANOL/WATER K_(OW)  10^(3.27) DISTRIBUTIONCOEFFICIENT MELTING POINT T_(M) 273.45 [K]

TABLE 17 INDOOR ENVIRONMENTAL BE- EXAMPLE OF HAVIOR PROPERTY OF COMPOUNDSYMBOL VALUE PHOTODEGRADATION CONSTANT IN AEROSOL PARTICLES K_(i) (i =8.67 × 10⁻³ [1/h] 2,3,8) AIR K₄ 1.05 × 10⁻¹ [1/h] FLOOR K₅ 1.60 × 10⁻³[1/h] WALL/CEILING K_(j) (j = 9.62 × 10⁻⁴ [1/h] 6,7) HALF-LIFE OFTRANSFERENCE TO AIR IN FLOOR τ₄₅ 36.0 [h] WALL τ₄₆ 43.2 [h] CEILING τ₄₇43.2 [h]

TABLE 18 EXAMPLE OF INDOOR ENVIRONMENT SYMBOL VALUE OIL ROOM SIZE V₄23.3 [m^(3]) BASE TEMPERATURE T  297 [K] RELATIVE HUMIDITY φ 60 [% RH]ABSOLUTE HUMIDITY H 1.19 × 10⁻² [kg-H₂O/ kg-dry air] VENTILATION RATE G1.58 [1/h] INDOOR VAPOR PRESSURE P∞   0 [Pa] IN PARTICLE - CONSTITUTINGSOLVENT AIR DIFFUSION D_(air) 1.84 × 10⁻² COEFFICIENT [m²/h] OILCOMPONENT CONTENT —   46 [%] (IN CASE OF TATAMI)   4 [%] (IN CASE OFFLOORING)   30 [%] (IN CASE OF WALLPAPER) WATER WET - BULB TEMPERATURET_(d) 294 [K] BASE VAPOR PRESSURE OF P∞ 1.89 × 10³ [Pa] WATER HERE, V₄ =L₄ × W₄ × HEIGHT.

TABLE 19 EXAMPLE OF PRODUCT PROPERTY SYMBOL VALUE OIL COMPOUND CONTENTC_(a) 1.33 × 10³ [g/m³] BASE (CONCENTRATION) SPRAY RATE — 0.45 [g/sec]PARTICLE CONSTITUTING SOLVENT PROPERTY VAPOR PRESSURE P_(d) 6.92 [Pa]MOLECULAR WEIGHT M_(d) 184.37 [g/mole] SPECIFIC GRAVITY ρ_(d) 7.56 × 10⁵[g/m³] DIAMETERS OF AEROSOL PARTICLE (3 KINDS) d₀₂ 50 [μm] d₀₈ 30 [μm]d₀₃ 10 [μm] DISTRIBUTIONS OF AEROSOL PARTICLES (3 KINDS) — 30 [%] (LARGEPARTICLE) — 60 [%] (MEDIUM PARTICLE) — 10 [%] (SMALL PARTICLE) WATERPARTICLE CONSTITUTING BASE SOLVENT PROPERTY VAPOR PRESSURE P_(d) 2.26 ×10³ [Pa] MOLECULAR WEIGHT M_(d) 18 [g/mole] SPECIFIC GRAVITY ρ_(d) 1 ×10⁶ [g/m³]

TABLE 20 SPRAY CONDITION EXAMPLE OF VALUE SPRAY TIME  10 [sec] SPRAYHEIGHT 1.6 [m]

Here, the examples of values in Tables 16 to 20 assume those of asix-mat room (9.72 [m²]) of a typical apartment in Japan in summer (seeFIG. 14).

Subsequently, using the primary condition, a secondary condition isdetermined by calculation (S2). The secondary condition comprises atemporally unchangeable definite factor condition (see Table 21)determined by the primary condition alone, and a temporal changecondition accompanying a temporal change (see Table 22). Theircalculations will be explained later in detail.

TABLE 21 DEFINITE FACTOR CONDITION SYMBOL NUMBER OF AEROSOL PARTICLESn_(0i) (i = 2,8,3) IMMEDIATELY AFTER SPRAYING EVAPORATION CONSTANT OFAEROSOL α PARTICLES VOLUME RATIO OF COMPOUND IN PRODUCT R_(a) DIFFUSIONCOEFFICIENT OF COMPOUND IN AIR D_(ca) SURFACE AREA OF FLOOR/WALL/CEILINGA_(j) (j = 5,6,7) DIFFUSION COEFFICIENT OF FLOOR/WALL/ D_(c) CEILINGFUGACITY CAPACITY OF AEROSOL PARTICLE Z_(i) (i = 2,8,3) AIR Z₄FLOOR/WALL/CEILING Z_(j) (j = 5,6,7)

TABLE 22 TEMPORAL CHANGE CONDITION SYMBOL AEROSOL PARTICLE DIAMETERd_(i) (i = 2,8,3) FALLING SPEED v_(i) (i = 2,8,3) FLOATING NUMBER n_(i)(i = 2,8,3) AEROSOL ZONE WIDTH L_(zi) (i = 2,8,3) TRANSFERENCE SPEED OFCOMPOUND IN AEROSOL PARTICLE k_(i) (i = 2,8,3) AIR k₄ FLOOR/WALL/CEILINGk_(j) (j = 5,6,7) TRANSFERENCE COEFFICIENT OF COMPOUNDD_(i4 (i = 2,8,3)) BETWEEN AEROSOL PARTICLE AND AIR TRANSFERENCECOEFFICIENT OF COMPOUND D_(4j) (j = 5,6,7) BETWEEN AIR ANDFLOOR/WALL/CEILING VOLUME OF AEROSOL PARTICLE V_(i) (i = 2,8,3) VOLUMEOF FLOOR/WALL/CEILING V_(j) (j = 5,6,7)

Using the secondary condition, seven kinds of Fugacity are calculated(S3). Namely, seven kinds of differential equations concerning thelarge, medium, and small particles 2, 8, and 3, air 4, floor 5, wall 6,and ceiling 7 are simultaneously formed and are solved byRunge-Kutta-Gill method, whereby seven kinds of Fugacity are computedover time. Here, an estimation nick time width (minute time unit) setwhen solving the differential equations is automatically set so as to bevaried in response to a fluctuation in mass balance of the compound.

At S4, using thus computed Fugacity (f_(i), i=2, 8, 3) of the small,medium, and large particles 2, 8, and 3, and Fugacity (f₄) of the air 4,temporal concentration of the compound in the air is computed; whereastemporal floor residual amount of the compound on the floor 5 iscomputed by use of Fugacity (f₅) of the floor 5.

At S5, it is judged whether or not to perform safety evaluation in thecase where the chemical is inhaled. If the safety evaluation ininhalation is to be performed, then an estimated exposure amount ininhalation indicating a degree of exposure upon inhalation of thecontaminated air is computed by use of the above-mentioned temporalconcentration in the indoor air (S6). Thereafter, an inhalation safetycoefficient is computed according to the estimated exposure amount ininhalation (S7). At S8, the inhalation safety coefficient is comparedwith a reference value defined in each country. If the inhalation safetycoefficient exceeds the reference value, it is judged that “there is noproblem in safety.” By contrast, if the inhalation safety coefficient islower than the reference value at S8, it is judged that “there is aproblem in safety,” and the operation returns to S1, where alteration ofthe primary condition such as alteration of compound, alteration ofchemical formulation, alternation of using condition, or the like isconsidered.

If the safety evaluation in inhalation is not selected at S5, calculatedis an estimated amount of percutaneous exposure indicating to whatextent the skin is exposed in contact with the floor 5 to which thechemical is attached (S9). Thereafter, at S10, it is judged whether toperform a percutaneous safety evaluation or not. If the percutaneoussafety evaluation is to be performed, a percutaneous safety coefficientis computed according to the estimated percutaneous exposure amount(S11). At S12, as with the safety evaluation in inhalation, thepercutaneous safety coefficient is compared with a reference valuedefined in each country, whereby the safety is evaluated. If there is aproblem in safety at S12, the operation returns to S1, where alterationof the primary condition is considered.

If the percutaneous safety evaluation is not selected at S10, calculatedat S13 according to the estimated percutaneous exposure amount is anestimated oral exposure amount indicating the degree of exposure in thecase where the chemical attached to a hand or the like is taken orally(S13). Subsequently, according to the estimated oral exposure amount, anoral safety coefficient is computed (S14). This oral exposure may occur,in particular, when an infant puts a chemical-attached hand into themouth. At S15, as with the safety evaluation in inhalation, the oralsafety coefficient is compared with a reference value defined in eachcountry, whereby the safety is evaluated. If there is a problem insafety at S15, the operation returns to S1, where alteration of theprimary condition is considered.

Finally, if it is judged to be safe at S8, S12, or S15, overall safetyis evaluated. Here, the sum of respective reciprocals of the previouslydetermined inhalation safety coefficient, percutaneous safetycoefficient, and oral safety coefficient is determined, and thereciprocal of thus determined value is defined as an overall safetycoefficient (S16). This overall safety coefficient is compared with areference value, whereby an evaluation similar to the previous safetyevaluation is effected (S17).

In the following, the above-mentioned steps of S2 to S4, 56, S7, S9,S11, S13, and S14 will be explained in detail.

(i) Secondary Condition Calculation (S2)

Calculations of the definite factor condition shown in Table 21 and thetemporal change condition shown in Table 22 will be explained.

The particle number (n_(0i), i=2, 8, 3) of the large, medium, and smallparticles 2, 8, and 3 immediately after spraying is determined from thespraying rate, particle diameter (d_(0i), i=2, 8, 3) immediately afterspraying, distributions of particles (three kinds), and spray time. Theparticle number (n_(0i)) is constant until the bottom of the sprayingzone (SZ_(i), i=2, 8, 3) reaches the floor 5.

According to surface temperature (T_(d)) of particles, properties ofparticle-constituting solvent (vapor pressure P_(d), molecular weightM_(d), and specific gravity ρ_(d)), and indoor environment (airdiffusion coefficient D_(air), vapor pressure P^(∞), and roomtemperature T^(∞)), the evaporation constant (α) of the large, medium,and small particles 2, 8, and 3 is defined as: $\begin{matrix}{\alpha = {\frac{4D_{air}M_{d}}{R\quad \rho_{d}}\left( {\frac{P_{d}}{T_{d}} - \frac{P\quad \infty}{T\quad \infty}} \right)}} & (28)\end{matrix}$

wherein R is a gas constant.

Here, the upper parts of the above-mentioned Tables 18 and 19 exemplifythe case where the spatially sprayed aerosol is of oil base. In thiscase, T^(∞) (temperature at the site far from aerosol particles) andT_(d) are set to room temperature (T), whereas P^(∞) (vapor pressure ofoil at the site far from aerosol particles) is set to zero.

In the case where the spatially sprayed aerosol is of water base, it isnecessary for P_(d), M_(d), ρ_(d), T_(d), and P^(∞) in expression (28)to be changed to values based on properties of water. Specifically, theabove-mentioned factor values when the room temperature (T) is 298 [K](=25° C.) and the relative humidity is 60[% RH] are exemplified in thelower parts of Tables 18 and 19.

Here, T_(d) can be determined, according to the room temperature (T) andrelative humidity (H), from “mass-based humidity table” disclosed in“Kagaku Kikai no Riron to Keisan (Theory and Calculation of ChemicalMachines)” (Second Edition) (Saburo Kamei ed., Sangyo Tosho) or thelike. On the other hand, P_(d) and P^(∞) can be computed from thefollowing expressions:

log₁₀ P _(d)=10.23−1750/(T _(d)−38)

log₁₀ P ^(∞)=8.23−1750/(T−38)+log₁₀ψ

wherein ψ is an indoor relative humidity.

From the vapor pressure (P^(s)) and melting point (T_(M)) of thecompound and surface temperature (T_(d)) of particles, Fugacity capacity(Z_(i), i=2, 8, 3) of the large, medium, and small particles 2, 8, and 3is expressed as: $\begin{matrix}\begin{matrix}{Z_{i} = \frac{6 \times 10^{6}}{P_{L}^{S}{RT}_{d}}} \\{P_{L}^{S} = {P^{S}\exp \quad \left\{ {6.79\left( {{T_{M}/T_{d}} - 1} \right)} \right\}}}\end{matrix} & (29)\end{matrix}$

Though the vapor pressure of the compound in a liquid state (P_(L) ^(s))is computed by use of T_(M) and T_(d) here; in the case where T_(M)cannot be obtained, P_(L) ^(s) may be set identical to the vaporpressure of the compound in a solid state (P^(s)).

From the room temperature (T), Fugacity capacity (Z₄) of the air 4 isexpressed as follows: $\begin{matrix}{Z_{4} = \frac{1}{RT}} & (30)\end{matrix}$

From the vapor pressure (P^(s)), water solubility (C^(s)), andoctanol/water distribution coefficient (K_(ow)) of the compound, andfrom the oil component content (ρ_(j), j=5, 6, 7) of the materialconstituting the floor 5, wall 6, and ceiling 7, Fugacity capacity(Z_(j), j=5, 6, 7) of the floor 5, wall 6, and ceiling 7 is expressedas:

Z _(j)=ρ_(j) K _(OW) C ^(S) /P ^(S)  (31)

Since the volume of particles decreases over time due to evaporation ofthe particle-constituting solvent component, during the evaporation ofparticle-constituting solvent component, using the diameter (d_(0i)) ofparticles immediately after spraying (t=0) and the evaporation constant(α) determined from expression (28), the diameter (d_(i), i=2, 8, 3) ofthe large, medium, and small particles 2, 8, and 3 at time t isrepresented as shown in the following expression (32):

d _(i) ={square root over (d_(0i) ²−2αt)}  (32)

d _(i) ={square root over (R_(a))} d _(0i)  (32′)

By contrast, the diameter (d_(i)) of particles after completeevaporation of the particle-constituting solvent component isrepresented as shown in the above expression (32′) by use of the ratioof volume of the compound in the product (R_(a)) and the diameter(d_(0i)) of particles immediately after spraying.

From the compound content (C_(a)) and specific gravity of the compound(ρ), the ratio of volume of the compound in the product (R_(a)) isexpressed as C_(a)/ρ.

Since movement of the particles is under the control of gravity and airresistance, according to Stokes' law using the specific gravity (ρ_(d))of the particle-constituting solvent and the diameter (d_(i)) ofparticles determined by expression (32), the falling speed (v_(i), i=2,8, 3) of the large, medium, and small particles 2, 8, and 3 beforecomplete evaporation of the particle-constituting solvent component isrepresented by the following expression (33): $\begin{matrix}{v_{i} = {{\frac{\rho_{d}{gS}_{c}}{18\quad \eta}d_{i}^{2}} = {{\beta \quad d_{i}^{2}} = {\beta \left( {d_{0i}^{2} - {2\quad \alpha \quad t}} \right)}}}} & (33) \\{S_{c} = {1 + {\frac{2}{7.6 \times 10^{7}d_{i}}\left\{ {6.32 + {2.01\quad {\exp \left( {{- 8.322} \times 10^{6}d_{i}} \right)}}} \right\}}}} & \left( 33^{\prime} \right) \\{v_{i} = {\left( {\rho/\rho_{d}} \right)\beta \quad d_{i}^{2}}} & \left( 33^{''} \right)\end{matrix}$

wherein g is gravitational acceleration, η is the coefficient ofviscosity of the air 4, S_(c) is a sliding correction coefficient, and,β is a speed coefficient. Here, while particles do not conform to theStokes' law when they become small, the sliding correction coefficient(S_(c)), which is a coefficient for correcting this phenomenon, isrepresented by the above expression (33′) according to the diameter(d_(i)) of particles determined by expression (32).

On the other hand, the falling speed (v_(i)) of the particles after thecomplete evaporation of particle-constituting solvent component isrepresented by the above expression (33″) using the specific gravity (ρ)of the compound, specific gravity (ρ_(d)) of the particle-constitutingsolvent, speed coefficient (β), and diameter (d_(i)) of particlesdetermined by expression (32′).

From the spray height, aerosol zone width (L_(zi)) determined byexpression (35) which will be mentioned later, falling speed (v_(i)) ofparticles determined by expression (33) or expression (33″), and theabove-mentioned particle number (n_(0i)) immediately after spraying, thefloating number (n_(i), i=2, 8, 3) of the large, medium, and smallparticles 2, 8, and 3 after the bottom of the spraying zone (SZ_(i))reaches the floor 5 is expressed as: $\begin{matrix}{n_{i} = {n_{0i}\left\lbrack {1 - {\frac{v_{i}}{L_{Zi}}\left( {t - t_{Xi}} \right)} - {Gt}} \right\rbrack}} & (34)\end{matrix}$

wherein t_(xi) is the time necessary for the bottom of the spraying zone(SZ_(i)) to reach the floor 5, and t<t_(xi). Here, G is the ventilationrate, taking account of the fact that the large, medium, and smallparticles 2, 8, and 3 not only disappear as attaching to the floor,wall, and ceiling but also are discharged outdoors by ventilation. Also,L_(Zi) is the dispersion width of suspended particles upon spraying,which may be either determined by expression (35) or simplified by useof the dispersion width immediately after dispersion as it is.

The width of aerosol zone (L_(Zi), i=2, 8, 3) is the width (height) ofthe spraying zone after the bottom of the spraying zone (SZ_(i)) reachesthe floor 5. Since the spraying zone (S_(zi)) is absorbed by the floor 5while changing the falling speed (v_(i)) of particles determined byexpression (33) or expression (33″), from the spray height and theabove-mentioned falling speed (v_(i)), the aerosol zone width is definedas: $\begin{matrix}{L_{Zi} = {\int_{t_{xi}}^{t_{yi}}{v_{i}{t}}}} & (35)\end{matrix}$

wherein t_(yi) is the time necessary for the spraying zone (SZ_(i)) tobe completely absorbed by the floor 5.

From the transference speed (k_(i), i=2, 8, 3) of the compound in thelarge, medium, and small particles 2, 8, and 3, transference speed (k₄)of the compound in the air 4, diameter (d_(i)) determined by expression(32) or (32′), and Fugacity capacity (Z_(i)) and Fugacity capacity (Z₄)determined by expressions (29) and (30), the transference coefficient(D_(i4), i=2, 8, 3) between the large, medium, and small particles 2, 8,and 3 and the air 4 is represented as follows: $\begin{matrix}{D_{i4} = \frac{1}{{1/\left( {k_{i}A_{i}Z_{i}} \right)} + {1/\left\{ {\left( {k_{4} + v_{i}} \right)A_{i}Z_{4}} \right\}}}} & (36)\end{matrix}$

wherein Ai (=πd_(i) ²) is the surface area of particles. From theventilation rate (G), the transference speed (k₄) of the compound in theair 4 is expressed as GV₄/A₄. From the transference speed (k₄) of thecompound in the air, the transference speed (k_(i)) of the compound inthe particles is expressed as k₄/100. Here, as shown in FIG. 14, theabove-mentioned A₄ is the cross-sectional area of the room with respectto the direction of movement of the air 4 (arrowed direction in thedrawing).

Using the diffusion coefficient (D_(c)) of compound in the floor 5, wall6, and ceiling 7, the transference speed (k_(j)) of the compound in thefloor 5, wall 6, and ceiling 7 is expressed as (D_(c)/t)^(0.5). Here,D_(c) can be computed as follows. Namely, D_(c) can be determined whenthe diffusion coefficient (D_(ca)) in the air is multiplied by 10⁻⁹,whereas D_(ca) can be computed from properties of the compound (e.g.,structural formula, molecular weight, and the like) according to Wikeand Lee method (“Handbook of Chemical Property Estimation Methods,”McGraw-Hill Book Company, 1982), for example.

From the half-life of transference to air (τ_(4j), j=5, 6, 7) in each ofthe floor 5, wall 6, and ceiling 7, room size (V₄), volume (V_(j)) ofthe floor 5, wall 6, and ceiling 7 determined by expression (39)mentioned later, and Fugacity capacity (z₄) and (z_(j)) determined byexpressions (30) and (31), the transference coefficient (D_(4j), j=5, 6,7) of the compound between the air 4 and the floor 5, wall 6, andceiling 7 is represented as the following expression (37):$\begin{matrix}{D_{4j} = \frac{0.693}{\tau_{4j}\left\{ {{1/\left( {V_{4}Z_{4}} \right)} + {1/\left( {V_{j}Z_{j}} \right)}} \right\}}} & (37) \\{D_{4j} = \frac{1}{{1/\left( {k_{4}A_{j}Z_{4}} \right)} + {1/\left( {k_{j}A_{j}Z_{j}} \right)}}} & \left( 37^{\prime} \right)\end{matrix}$

The above-mentioned transference coefficient (D_(4j)) may also bedetermined by the expression represented by the above-mentionedexpression (37′) from the speed of the compound in the air (k₄), speed(k_(j)) of the compound in the floor 5, wall 6, and ceiling 7, surfacearea (A_(j), j=5, 6, 7) of the floor 5, wall 6, and ceiling 7, andFugacity capacity (Z₄) and (Z_(j)) determined by expressions (30) and(31). The surface area (A_(j)) of each of the floor 5, wall 6, andceiling 7 is determined by the size of the room (V₄=L₄×W₄×height).

Here, the half-life of transference to air (τ_(4j)) in expression (37)is hard to actually measure and varies under various conditions, thusmaking it difficult to determine an accurate value thereof. By contrast,all the parameters in expression (37′) can be easily determined bycalculation without necessitating measurement. Accordingly, thetransference coefficient (D_(4j)) is more preferably determined byexpression (37′) than by expression (37).

Using the diameter (d_(i)) of particles determined by expression (32) orexpression (32′), the volume (V_(i), i=2, 8, 3) of the large, medium,and small particles 2, 8, and is expressed by: $\begin{matrix}{V_{i} = {\frac{\pi}{6}d_{i}^{3}}} & (38)\end{matrix}$

Assuming that each of the floor 5, wall 6, and ceiling 7 before sprayingthe chemical is like a thin film and that, as the chemical infiltratesinto the film, its thickness increases so as to enhance the volumethereof; from the surface area (A_(j)) of the floor 5, wall 6, andceiling 7 and diffusion coefficient (D_(c)) of the compound in the floor5, wall 6, and ceiling 7, the volume (V_(j), j=5, 6, 7) of floor 5, wall6, and ceiling 7 becomes:

V _(j)=2{square root over (D _(c) t)}A _(j)  (39)

(ii) Fugacity Calculation (S3)

The behavior of the compound in the large, medium, and small particles2, 8, and 3 is expressed in the form of differential equation concerningFugacity (f_(i)) as: $\begin{matrix}\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{i}}{t}V_{i}Z_{i}} = {\frac{\pi}{2}\alpha \quad d_{i}Z_{i}f_{i}}} & {{V\text{-}{change}}} \\{{- {D_{i4}\left( {f_{i} - f_{4}} \right)}}} & {{{Transference}(4)}} \\{{{- K_{i}}V_{i}Z_{i}f_{i}}} & {{Degradation}}\end{matrix} & (40)\end{matrix}$

Here, the terms of V-change, Transference (4), and Degradationrespectively indicate volume change (decrease over time) of the large,medium, and small particles 2, 8, and 3, amount of transference of thecompound between the particles and the air 4, and change in amount ofphotodegradation of the compound. Here, among the photodegradationconstants shown in the above-mentioned Table 17, it is difficult toactually measure the photodegradation constant (K₄) of the compound inthe air, whereby it is not usually easy to determine this value.Therefore, when the actually measured value is unavailable, it may bedetermined as being computed by Atmospheric Oxidation program (Atkinsonet al., 1984, Chem. Rev. Vol. 84, pp.437-470) using the structuralformula of the compound. Also, the degradation constant in the particlesand in the interior materials (floor 5, wall 6, and ceiling 7) may beset to zero in view of the safety of inhabitants when the actuallymeasured values are unavailable. Here, the term of V-change is effectiveonly while the particle-constituting solvent component is evaporating,whereas Fugacity (f_(i)) is effective only while the spraying zone(SZ_(i)) exists.

The behavior of the compound in the air 4 is expressed in the form ofdifferential equation concerning Fugacity (f₄) as: $\begin{matrix}\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{4}}{t}V_{4}Z_{4}} = {{- {GV}_{4}}Z_{4}f_{4}}} & {{Ventilation}} \\{{- {\sum\limits_{{i = 2},8,3}{n_{i}{D_{i4}\left( {f_{4} - f_{i}} \right)}}}}} & {{{Transference}(i)}} \\{{- {\sum\limits_{j = 5}^{7}{D_{4j}\left( {f_{4} - f_{j}} \right)}}}} & {{{Transference}(j)}} \\{{{- K_{4}}V_{4}Z_{4}f_{4}}} & {{{Degradati}\quad {on}}}\end{matrix} & (41)\end{matrix}$

Here, the terms of Ventilation, Transference (i), Transference (j), andDegradation respectively indicate amount of discharge of the compoundoutdoors, amount of transference of the compound between the air 4 andthe particles, amount of transference between the air 4 and the floor 5,wall 6, and ceiling 7, and change in amount of photodegradation of thecompound.

The behavior of the compound in the floor 5, wall 6, and ceiling 7 isexpressed in the form of differential equation concerning Fugacity (f₅),(f₆), (f₇) as: $\begin{matrix}\begin{matrix}{{\frac{f_{5}}{t}V_{5}Z_{5}} = {{{- \sqrt{D_{c}/t}}A_{5}Z_{5}f_{5}} +}} & {{V\text{-}{change}}} \\{{F\text{-}{change}{~~~}\gamma_{5}{\sum\limits_{{i = 2},8,3}{\frac{n_{01}}{L_{zi}}v_{i}V_{i}Z_{i}f_{i}}}} -} & {{{Deposition}(i)}} \\{{{D_{45}\left( {f_{5} - f_{4}} \right)} -}} & {{{Transference}(4)}} \\{{K_{5}V_{5}Z_{5}f_{5}}} & {{Degradation}}\end{matrix} & (42) \\\begin{matrix}{{\frac{f_{6}}{t}V_{6}Z_{6}} = {{{- \sqrt{D_{c}/t}}A_{6}Z_{6}f_{6}} +}} & {{V\text{-}{change}}} \\{{F\text{-}{change}{\quad }\gamma_{6}{\sum\limits_{{i = 2},8,3}{\frac{n_{01}}{L_{zi}}v_{i}V_{i}Z_{i}f_{i}}}} -} & {{{Deposition}(i)}} \\{{{D_{46}\left( {f_{6} - f_{4}} \right)} -}} & {{{Transference}(4)}} \\{{K_{6}V_{6}Z_{6}f_{6}}} & {{Degradation}}\end{matrix} & (43) \\\begin{matrix}{{\frac{f_{7}}{t}V_{7}Z_{7}} = {{{- \sqrt{D_{c}/t}}A_{7}Z_{7}f_{7}} +}} & {{V\text{-}{change}}} \\{{F\text{-}{change}{\quad }\gamma_{7}{\sum\limits_{{i = 2},8,3}{\frac{n_{01}}{L_{zi}}v_{i}V_{i}Z_{i}f_{i}}}} -} & {{{Deposition}(i)}} \\{{{D_{47}\left( {f_{7} - f_{4}} \right)} -}} & {{{Transference}(4)}} \\{{K_{7}V_{7}Z_{7}f_{7}}} & {{Degradation}}\end{matrix} & (44)\end{matrix}$

Here, the terms of V-change, Transference (4), and Degradation in eachexpression respectively indicate volume change (increase over time) ofthe floor 5, wall 6, and ceiling 7, amount of transference of thecompound between the floor 5, wall 6, ceiling 7 and the air 4, andchange in amount of photodegradation of the compound. Also, Deposition(i) indicates attachment accompanying the falling of the particles.Here, γ₅, γ₆, and γ₇ indicate ratios of the large, medium, and smallparticles 2, 8, 3 attaching to the floor 5, wall 6, and ceiling 7,respectively, and mainly depend on the ventilation rate (e.g., when theventilation rate is 1.58 [1/hour], γ₅=0.93, γ₆=0.06, γ₇=0.01). As γ₅,γ₆, and γ₇ are introduced, the behavior of the compound can be estimatedaccurately. When γ₅, γ₆, and γ₇ are unavailable, it is preferable topresume the worst case in terms of safety evaluation and performcalculation with γ₅=1, γ₆=0, and γ₇=0.

The above-mentioned seven kinds of differential equations (40) to (44)are simultaneously formed and are solved by Runge-Kutta-Gill method, soas to compute Fugacity (f₂ to f₈).

When solving these simultaneous differential equations, it is necessaryto set an estimation nick time width (dt) which is a minute time unit.Namely, the estimation nick time width is used such that solutions ofthe simultaneous differential equations are initially determined at atime (t₀), and then solutions of the simultaneous differential equationsare determined at a time (t₀+dt) to which the estimation nick time widthis added. As solutions are obtained while estimation nick time widthsare successively added, temporally changing Fugacity can be determined.Theoretically, as the set time of the estimation nick time width isshorter, more accurate solutions can be obtained, though necessitating avery long calculation time. By contrast, when the set time is too long,solutions tend to diverge, thereby generating errors.

Therefore, in the present invention, the estimation nick time width isset shorter when a very large change occurs in a chemical, whereas it isset longer when there is no large change.

Specifically, mass balance is always confirmed such that the amount ofinput of the chemical and the resulting solution coincide with eachother, and the estimation nick time width is set longer when the massbalance does not fluctuate greatly, whereas it is set shorter when themass balance starts fluctuating. For example, when the fluctuation ofmass balance is set to an accuracy of ±5%, the estimation nick timewidth is always set so as to constantly satisfy the relationship of:

compound input amount/(existing amount+degrading amount+dischargingamount)=0.95 to 1.05

namely, such that the fluctuation of mass balance lies within the rangeof ±5%.

Here, the above-mentioned compound input amount is determined by thecompound content (C_(a)), spray rate, and spray time. Since the temporalamounts of compound in the seven kinds of media are determined by thesimultaneous differential equations, they are summed up so as to computethe existing amount as follows: $\begin{matrix}\left. \begin{matrix}{{{existing}\quad {amount}} = {{\sum\limits_{{i = 2},8,3}{n_{i}f_{i}V_{i}Z_{i}}} + {\sum\limits_{k = 4}^{7}{f_{k}V_{k}Z_{k}}}}} \\{{{degrading}\quad {amount}} = {{\sum\limits_{{i = 2},8,3}{n_{i}K_{i}f_{i}V_{i}Z_{i}}} + {\sum\limits_{k = 4}^{7}{K_{k}f_{k}V_{k}Z_{k}}}}} \\{{{discharging}\quad {amount}} = {{GV}_{4}Z_{4}f_{4}}}\end{matrix} \right\} & (45)\end{matrix}$

The degrading amount and discharging amount are as represented above.

With reference to the flowchart of FIG. 5, the method of setting theestimation nick time width (dt) will be explained.

First, an initial value of estimation nick time width (dt) is inputted(S21). Then, an upper limit set value (e.g., 0.1[%]) which is the upperlimit of difference in mass balance, and a lower limit set value (e.g.,10⁻⁶[%]) which is the lower limit of difference in mass balance areinputted (S22). Thereafter, Fugacity and mass balance at t=t₀ arecalculated (S23 and S24), and Fugacity and mass balance at t=t+dt (ort₀+dt) are calculated (S25 and S26).

It is judged whether the fluctuation in mass balance is within the rangeof ±5% or not (S27). If the fluctuation in mass balance is within therange of ±5%, it is judged whether the difference between the massbalance at t=t (or t₀) and the mass balance at t=t+dt (or t₀+dt) is atleast the upper limit set value or not (S28). If it is judged to be atleast the upper limit set value at S28, then solutions become moreaccurate when the estimation nick time width (dt) is made shorter. Inthis case, the estimation nick time width (dt) is multiplied by ½ so asto change its setting (S29). When the difference is judged to be smallerthan the upper limit set value at S28, it is judged at S30 whether thedifference between the mass balance at t=t (or t₀) and the mass balanceat t=t+dt (or t₀+dt) is at most the lower limit set value or not.

When the mass balance difference is not greater than the lower limit setvalue at S30, since solutions are not influenced by longer estimationnick time width (dt), the estimation nick time width (dt) is doubled soas to change its setting (S31). Subsequently, it is judged whether theestimation nick time width (dt) changed at S31 is at most a maximumvalue (e.g., 0.1 [hour]) of estimation nick time width (dt) or not(S32). When the estimation nick time width (dt) is not greater than themaximum value at S32, since solutions do not diverge, the estimationnick time width (dt) set at S31 is used. When the estimation nick timewidth (dt) is greater than the maximum value at S32, since solutions maydiverge, the estimation nick time width (dt) is reset to the maximumvalue (S33). When the mass balance difference is greater than the lowerlimit set value at the above-mentioned S30, namely, when it lies betweenthe lower limit set value and upper limit set value, the calculationsare continued without changing the estimation nick time width (dt).

After the step of S29, S30, S32, or S33, the operation returns to S25 soas to effect calculation again, and this process is repeated till theaimed time is attained.

When the fluctuation in mass balance exceeds the range of ±5% at S27, onthe other hand, the mass balance fluctuation is so much that calculationis preferably effected with an estimation nick time width (dt) shorterthan that in the case where the fluctuation is within the range of ±5%.Accordingly, the calculation is stopped once (S34), the lower limit setvalue is reset to a lower level (S35), and then the operation returns tothe step of S23.

Thus, when the estimation nick time width is variably set without beingheld constant, while monitoring the mass balance fluctuation, Fugacitycan be computed accurately and efficiently.

(iii) Computation of Temporal Concentration in Indoor Air and FloorResidual Amount (S4)

The temporal concentration of the compound in the indoor air is computedwhen Fugacity (f_(i)) of the large, medium, and small particles 2, 8,and 3, determined by the above-mentioned item (ii), multiplied by theirFugacity capacity (Z_(i)), and Fugacity (f₄) of the air 4 multiplied byFugacity capacity (Z₄) of the air 4 are summed up. Here, the largeparticles 2 or medium particles 8 may not be inhaled by a human bodydepending on the kind of chemical. In such a case, calculation iseffected by use of Fugacity (f₃) of the small particles 3 alone, forexample.

The floor residual amount of the compound is computed when Fugacity (f₅)of the floor 5 is multiplied by Fugacity capacity (Z₅) of the floor 5.

(iv) Calculation of Estimated Exposure Amount in Inhalation andInhalation Safety Coefficient (S6 and S7)

The above-mentioned temporal concentration in the indoor air forms acurve shown in FIG. 3A, for example. This concentration curve isintegrated, an accumulated concentration of the compound during aspecific period (t₁ to t₂) is determined (see FIG. 3B), and the meanconcentration in the indoor air is computed from thus determined value.While an arbitrary period is set as the specific period depending on theobject, an appropriate period is usually set in view of the method ofuse of the product and the test period of toxicity data.

Then, according to the above-mentioned mean concentration in the indoorair, amount of respiration, and exposure time, the estimated exposureamount in inhalation is determined. Namely, calculation of:

estimated exposure amount in inhalation [mg/kg/day)=mean concentrationin indoor air [mg/m³]×amount of respiration [m³/kg/min]×exposure time[min/day]

is effected. Here, as the above-mentioned amount of respiration, apublished value or actually measured value may be used. Also, whenamounts of respiration are respectively set for adult and child, moreappropriate estimated exposure amounts in inhalation can be obtained. Inthe case where the inhaled harmful material is not totally absorbed intothe body but is partially discharged by respiration, a more appropriateestimated exposure amount in inhalation can be obtained when theinhalation ratio is taken into account.

The inhalation safety coefficient is computed from a non-influentialamount concerning inhalation toxicity examined by an animal experimentbeforehand and the estimated exposure amount in inhalation determinedabove. Namely, it is expressed as:

inhalation safety coefficient=inhalation non-influential amount[mg/kg/day]/estimated exposure amount in inhalation [mg/kg/day]

(v) Calculation of Estimated Percutaneous Exposure Amount andPercutaneous Safety Coefficient (S9 and S11)

The above-mentioned floor residual amount forms a curve such as thatshown in FIG. 4A, for example. This residual amount curve is integrated,the accumulated residual amount of the compound during a specific period(t₁ to t₂) is determined (see FIG. 4B), and the mean residual amount iscomputed from thus determined value. While an arbitrary period is set asthe specific period depending on the object, an appropriate period isusually set in view of the method of use of the product and the testperiod of toxicity data.

Then, according to the mean floor residual amount, skin attachmentratio, contact area, and body weight, the estimated percutaneousexposure amount is determined. Namely, calculation of:

estimated percutaneous exposure amount [mg/kg/day)=(mean floor residualamount [mg/m²]×skin attachment ratio [%]×contact area [m²/day])/bodyweight [kg]

is effected. Here, as the contact area, a published value (e.g., 4[m²/day]) may be used. The skin attachment ratio is a ratio of thecompound attaching to the skin when the latter is in contact with thefloor 5 where the compound exists. As this value, a published value or avalue experimentally obtained from a model may be used.

A model experiment method for the skin attachment ratio is as follows. Aweight (8 cm×8 cm×8 cm; 4.2 kg) is placed on a denim cloth (8 cm×10 cm)with a pressure similar to that of an infant in contact with a floor,and the denim cloth is pulled on the floor at a speed (120 cm/15 sec)similar to the moving speed of the infant. The denim and floor areanalyzed so as to compute the compound contained in the denim and floor.From the ratio therebetween, the skin attachment ratio is obtained. Ithas been confirmed that the skin attachment ratio obtained by thismethod is identical to or slightly higher than that determined fromanalyzed values of a hand and a floor when the hand is actually pressedagainst the floor, thereby proving this model experiment method to beuseful for evaluating exposure of inhabitants.

The percutaneous safety coefficient is computed from the non-influentialamount concerning percutaneous toxicity examined by an animal experimentbeforehand and the estimated percutaneous exposure amount determinedabove. Namely, it is expressed as:

percutaneous safety coefficient=percutaneous non-influential amount[mg/kg/day]/estimated percutaneous exposure amount [mg/kg/day]

Nevertheless, in general, percutaneous non-influential amount has notoften been determined, and there are not many published values.Accordingly, a more accurate value can be determined from the estimatedpercutaneous exposure amount, and oral non-influential amount andpercutaneous absorption ratio for which many published values exist,according to the following expression:

percutaneous safety coefficient=oral non-influential amount[mg/kg/day]/(estimated percutaneous exposure amount[mg/kg/day]×percutaneous absorption ratio [%])

Here, when the percutaneous absorption ratio is unknown, employed is anational guideline (e.g., 10%) which usually exists.

(vi) Calculation of Estimated Oral Exposure Amount and Oral SafetyCoefficient (S13 and S14)

From the estimated percutaneous exposure amount obtained in theabove-mentioned item (v), hand surface area ratio, and oral transferenceratio, the estimated oral exposure amount from hand to mouth isdetermined. Namely, calculation of:

estimated oral exposure amount (mg/kg/day]=estimated percutaneousexposure amount [mg/kg/day]×hand surface area ratio [%]×oraltransference ratio [%]

is effected. Here, the hand surface area ratio is expressed by (handsurface area/body surface area), for which a published value (e.g.,5[%]) may be used. The oral transference ratio is a hypothetical value,which is set to 100%, for example.

In the case where oral exposure might occur via tableware or foodcontaminated with the residually sprayed compound, it is required thatthe estimated oral exposure amount from tableware or food to mouth beadded to the estimated oral exposure amount from hand to mouth to yieldthe total estimated oral exposure amount. For example, the estimatedoral exposure amount from tableware is obtained when, according to thetableware residual amount indicating the amount of the harmful materialremaining in tableware, tableware use area which is the sum of tablewaresurface areas, and oral transference ratio from tableware, calculationof:

estimated oral exposure amount [mg/kg/day]=tableware residual amount[mg/m²]×tableware use area [m²/day]×oral transference ratio [%]/bodyweight [kg]

is effected. Here, the tableware residual amount is expressed by (meanfloor residual amount×tableware contamination ratio). As the tablewarecontamination ratio, an actually measured value (e.g., 9%) or ahypothetical value may be used.

The oral safety coefficient is computed from the non-influential amountconcerning oral toxicity examined by an animal experiment beforehand andthe estimated oral exposure amount determined above. Namely, it isexpressed as:

oral safety coefficient=oral non-influential amount[mg/kg/day]/estimated oral exposure amount [mg/kg/day]

As mentioned in the foregoing, in the method of estimating an indoorbehavior of a pesticidal compound in this embodiment, when a chemicalcontaining the above-mentioned compound is spatially sprayed,differential equations concerning Fugacity of the large, medium, andsmall particles 2, 8, and 3, air 4, floor 5, wall 6, and ceiling 7 aresimultaneously formed and are solved, and the indoor behavior of thecompound is estimated according to thus obtained solution. Here, theestimation nick time width is variably set, while constantly confirmingmass balance of the compound indoors after the spraying, so that theamount of input of the chemical indoors and the resulting solutioncoincide with each other.

Accordingly, since mass balance of the compound after the spraying isalways monitored such that the amount of input of the compound indoorsand the resulting solution coincide with each other, thereby varying theestimation nick time width; the estimation nick time width is set longerwhen the mass balance fluctuates a little, whereas it is set shorterwhen the mass balance starts fluctuating greatly. Namely, when solvingsimultaneous differential equations including a parameter accompanyingtemporal change, the estimation nick time width is automatically set inresponse to the fluctuation in mass balance. Consequently, whenprocessed by a computer, an accurate solution can be obtained in a shorttime.

The method of evaluating safety of a pesticidal compound in accordancewith this embodiment uses the estimated result mentioned above toevaluate the safety of the compound with respect to the human body whenthe chemical is spatially sprayed.

Accordingly, the safety of the compound with respect to the human bodycan be evaluated accurately in a short time. As a consequence, whenformulating a chemical such as insecticide containing the compound,simulation can be easily repeated while changing conditions, therebymaking it easier to formulate a chemical having a high safety conformingto the aimed object.

Though the kind of the floor 5 is assumed to be tatami in thisembodiment, differential equations similar to those mentioned above mayalso be formed in the case of flooring. In this case, however, whendetermining fugacity capacity (Z₅) of the floor 5 in equation (31), itis necessary for the particle-constituting solvent component content(see Table 18) to be changed from that of tatami to that of flooring.

Though Fugacity is determined by use of Runge-Kutta-Gill method in thisembodiment, other methods may be used for solving differentialequations. Runge-Kutta-Gill method, however, is preferably used since aprogram for the above-mentioned differential equations can be easilymade by Basic. Also in the case where differential equations are solvedby a method other than Runge-Kutta-Gill method, similar effects can beobtained when the estimation nick time width is set as mentioned above.

In the following, examples (Examples 6 to 10) of the method ofsimulating an indoor behavior of a pesticidal compound in accordancewith the third embodiment will be explained.

The evaluation of the method of estimating an indoor behavior of apesticidal compound in these examples is effected, under variousexperimental conditions (Example 6 to Example 10), as the resultsobtained by estimation and the actually measured values obtained bymeasurement of the actual indoor behavior of the compound are comparedwith each other. The respective experimental conditions of Examples areas follows.

Example 6 uses, as the spatially sprayed chemical, an oil-basedinsecticide containing pyrethroid. The indoor environment is a typicalapartment room (3.6 [m]×3.6 [m]×2.4 [m]) in Japan. The floor is aflooring in which a wooden floor is covered with a polyurethane resin,whereas the wall and ceiling are covered with a polychlorovinylwallpaper. The windows are completely closed during and after thespatial spraying. The spatial spraying is uniformly effected for 10seconds at a height of 1.6 [m] from the floor. The other conditions areshown in Tables 16 to 20.

The conditions of Example 7 are the same as those of Example 6 exceptthat its ventilation rate is 0.5 [1/hour].

The conditions of Example 8 are the same as those of Example 6 exceptthat its ventilation rate is 4.1 (1/hour].

The conditions of Example 9 are the same as those of Example 6 exceptthat the windows are opened for only 5 minutes after 5 minutes from thespraying.

The conditions of Example 10 are the same as those of Example 6 exceptthat the windows are opened for only 2 hours after 5 minutes from thespraying.

FIGS. 12A and 12B show the simulation results and actually measuredvalues of the compound concentration in the air under the respectiveconditions of the above-mentioned Examples. Also, FIG. 12C shows thesimulation results of the residual amounts in floor and ceiling inExample 6. In these charts, solid lines, dotted lines, and dashed linesindicate simulation results, whereas plotted points indicate actuallymeasured values.

From the above-mentioned results, it can be seen that the estimatedresults according to the method of simulating an indoor behavior of thecompound in accordance with the present invention are very close to theactually measured values.

(4) Fourth Embodiment

With reference to the drawings, the fourth embodiment of the presentinvention will be explained in the following. The method of simulatingan indoor behavior of a pesticidal compound in accordance with thisembodiment estimates the behavior of the compound in the case where thefloor in the third embodiment is constituted by a rug having ears offiber. For convenience of explanation, members identical to those shownin the drawings of the above-mentioned third embodiment will be referredto with numerals or letters identical thereto, without theirexplanations provided. Explained here is a case where the kind of flooris a carpet. Accordingly, only the portion different from the thirdembodiment will be explained.

First, the carpet is modeled as shown in FIGS. 13A, 13B, and 13C.Namely, the carpet is divided into a plurality of carpet fibers (ears offiber) planted on a substrate and space portions existing between thefibers. When a chemical is spatially sprayed in a room in which such acarpet covers the whole floor surface, as particles fall on the carpet,the chemical infiltrates into the carpet fiber and accumulates in thespace portion.

While the method of simulating an indoor behavior of a pesticidalcompound in accordance with this embodiment also conforms to theflowchart of FIG. 1, at S1, as the primary condition, the carpet-relatedprimary condition shown in Table 23 is added to the primary condition ofthe third embodiment (see Tables 16 to 20). Here, the cross-sectionalarea (A_(c)) of the space portion of the carpet refers to the area inwhich the space portion is in contact with the indoor air (see FIGS.13A, 13B, and 13C).

TABLE 23 CARPET-RELATED EXAMPLE PRIMARY CONDITION SYMBOL OF VALUE CARPETCROSS - SECTIONAL AREA OF A_(c) 1.6 × 10⁻³ SPACE PORTION OF CARPET[m²/m² FLOOR] AREA IN WHICH CARPET FIBER IS A_(c5) 0.192 IN CONTACT WITHCOMPOUND IN [m²/m² FLOOR] SPACE PORTION AREA IN WHICH CARPET FIBER ISA_(a5) 1.19 IN CONTACT WITH COMPOUND [m²/m² FLOOR] PRODUCT PROPERTYCONTENT OF SOLVENT (XYLENE) C_(sd) CONTAINED IN PRODUCT DILUTION OFPRODUCT X_(sol)

The examples of values in Table 23 are based on the values shown inFIGS. 13A, 13B, and 13C. Here, one space portion is set to a size of 0.1[mm]×0.1 [mm]×3 [mm], and one square of carpet fiber is set to a size of2.5 [mm]×2.5 [mm]×3 [mm]. Also, it is assumed that 16 [pieces] of carpetfiber exist in 1 [cm²].

In this case, the individual parameters can be determined as:$\begin{matrix}{A_{c} = {\left( {{0.1\quad\lbrack{mm}\rbrack} \times {0.1\quad\lbrack{mm}\rbrack} \times {16\quad\lbrack{pieces}\rbrack}} \right)\text{/}{1\quad\lbrack{cm}\rbrack}}} \\{= {1.6 \times {10^{- 3}\quad\left\lbrack {m^{2}\text{/}m^{2}\quad {floor}} \right\rbrack}}} \\{A_{c5} = {\left( {{0.1\quad\lbrack{mm}\rbrack} \times {3\quad\lbrack{mm}\rbrack} \times {4\quad\lbrack{faces}\rbrack} \times {16\quad\lbrack{pieces}\rbrack}} \right)\text{/}{1\quad\lbrack{cm}\rbrack}}} \\{= {0.192\quad\left\lbrack {m^{2}\text{/}m^{2}\quad {floor}} \right\rbrack}} \\{A_{5} = {1 - A_{c}}} \\{= {1 - {1.6 \times {10^{- 3}\quad\left\lbrack {m^{2}\text{/}m^{2}\quad {floor}} \right\rbrack}}}} \\{A_{a5} = {A_{5} + A_{c5}}} \\{= {1.19\quad\left\lbrack {m^{2}\text{/}m^{2}\quad {floor}} \right\rbrack}}\end{matrix}$

Here, A₅ is the area in which the carpet fibers in 1 [m²]are in contactwith the indoor air.

As the secondary condition at S2, the carpet-related secondary conditionshown in Table 24 is added to the secondary condition of the thirdembodiment. Here, k₅ and V₅, which are respectively transference speedof the compound in the floor and the volume of the floor in the thirdembodiment (see Table 22), are respectively replaced by the transferencespeed of the compound in the carpet fiber and the volume of the wholefiber of the carpet.

TABLE 24 CARPET - RELATED SECONDARY CONDITION SYMBOL DEFINITE FACTORCONDITION EVAPORATION CONSTANT OF CHEMICAL R_(d) IN SPACE PORTIONHUMIDITY AT TEMPERATURE (T_(d)) OF SPACE H_(m) PORTION VOLUME OF WHOLEFIBER OF CARPET V₅ TRANSFERENCE SPEED OF COMPOUND IN PRODUCT k_(c)PROPERTY CHANGE CONSTANT OF PRODUCT a TEMPORAL CHANGE CONDITIONTRANSFERENCE COEFFICIENT OF COMPOUND D_(c4) BETWEEN CHEMICAL IN SPACEPORTION AND AIR TRANSFERENCE COEFFICIENT OF COMPOUND D_(c5) BETWEENCHEMICAL IN SPACE PORTION AND CARPET FIBER VOLUME OF CHEMICAL IN SPACEPORTION V_(c) FUGACITY CAPACITY OF CHEMICAL IN Z_(c) SPACE PORTION

A method of computing the definite factor conditions and temporal changeconditions shown in the above-mentioned Table 24 will be explainedhereinafter as exemplified by the case using an aqueous aerosol, i.e.,case where the particle-constituting solvent is water.

From the cross-sectional area (A_(c)) of the space portion, roomtemperature (T), and humidity (H), the evaporation constant (R_(d)) ofthe chemical entered into the space portion of the carpet is expressedas:

R _(d) =A _(c) h(H _(m) −H)/C _(H)

C _(H)=0.24+0.46H

h=3.06×10⁻⁴(T−T _(d))^(1/3)  (46)

wherein T_(d) is the temperature of the space portion of the carpet(corresponding to the wet-bulb temperature), and H_(m) is the humidity(corresponding to the saturated humidity at the wet-bulb temperature) ofthe space portion at T_(d). Here, T_(d) and H_(m) can be determined fromthe above-mentioned “mass-based humidity table” according to the roomtemperature (T) and humidity (H). In the case of an oil-based product(aerosol), while the vapor constant of the chemical can be computed whenproperties of the water and oil are compared with each other and thenare multiplied by R_(d), R_(d)=0 may be assumed in the case where theevaporation of the oil is slow.

From the diffusion coefficient (D_(c)) and the area (A_(a5)) in whichthe carpet fiber is in contact with the compound, the volume (V₅) of thewhole fiber of the carpet is determined as:

V ₅=2{square root over (D_(c) t)}A_(a5)  (47)

The transference speed (k_(c)) of the compound in the product isexpressed as k₄/100 by use of k₄ (=GV₄/A₄) which indicates thetransference speed of the compound in the indoor air.

From the above-mentioned transference speed (k_(c)) of the compound inthe product, transference speed (k₄) of the compound in the indoor air,floor size (L₄×W₄), cross-sectional area (A_(c)) of the space portion,Fugacity capacity (Z_(c)) of the chemical in the space portiondetermined by expression (50) which will be mentioned later, andFugacity capacity (Z₄) of the air determined by expression (30) of thethird embodiment, the transference coefficient (D_(c4)) of the compoundbetween the chemical in the space portion of the carpet and the air isexpressed as: $\begin{matrix}{D_{c4} = \frac{1}{{1/\left( {k_{c}A_{c}L_{4}W_{4}Z_{c}} \right)} + {1/\left( {k_{4}A_{c}L_{4}W_{4}Z_{4}} \right)}}} & (48)\end{matrix}$

From the transference speed (k_(c)) of the compound in the product,diffusion coefficient (D_(c)), floor size (L₄×W₄), area (A_(c5)) inwhich the carpet fiber is in contact with the compound in the spaceportion, Fugacity capacity (Z_(c)) of the chemical in the space portion,and Fugacity capacity (Z₅) of the floor determined by expression (31) ofthe third embodiment, the transference coefficient (D_(c5)) of thecompound between the chemical in the space portion and the carpet fiberis expressed as: $\begin{matrix}{D_{c5} = \frac{1}{{1/\left( {k_{c}A_{c5}L_{4}W_{4}Z_{c}} \right)} + {1/\left( {k_{5}A_{c5}L_{4}W_{4}Z_{5}} \right)}}} & (49)\end{matrix}$

wherein the transference speed (k₅) of the compound within the carpetfiber is expressed as (D_(c)/t)^(0.5).

The volume (V_(c)) of the chemical in the space portion is determinedfrom the floor size (L₄×W₄), spray rate, content (C_(ad)) of the solvent(Xylene) contained in the product, dilution (X_(sol)) of the product,and evaporation constant (R_(d)) of the chemical in the space portiondetermined by expression (46).

From the vapor pressure (P^(s)), water solubility (C^(s)), andoctanol/water distribution coefficient (K_(ow)) of the compound, andproperty change constant (a) of the product, Fugacity capacity (Z_(c))of the chemical in the space portion is expressed as:

Z _(c)=(e ^(−at) K _(OW)+1−e ^(−at))C ^(S) /P ^(S)  (50)

Here, the property change constant (a) of the product can be computedaccording to the evaporation constant (R_(d)) of the chemical in thespace portion determined by expression (46), content (C_(sd)) of thesolvent (Xylene) contained in the product, and dilution (X_(sol)) of theproduct. Namely, Fugacity capacity (Z_(c)) of the chemical in the spaceportion is also expressed as:

Z _(c)=[(ratio of organic solvent in product)K _(ow)+(ratio of water inproduct)]×C ^(s) /P ^(s)

By simultaneously forming this expression and the above-mentionedexpression (50), the property change constant (a) of the product iscomputed. Here, in the case of the oil-based product (aerosol), Fugacitycapacity (Z_(c)) of the chemical in the space portion is given byexpression (31) of the third embodiment from the vapor pressure (P^(s)),water solubility (C^(s)), and octanol/water distribution coefficient(K_(ow)) of the compound.

Consequently, the behavior of the compound in the space portion of thecarpet is expressed in the form of differential equation concerningFugacity (f_(c)) as: $\begin{matrix}\begin{matrix}{{\frac{f_{c}}{t}V_{c}Z_{c}} = {{\gamma_{5}{\sum\limits_{{i = 2},8,3}{n_{i}v_{i}A_{c}V_{i}Z_{i}{f_{i}/L_{zi}}}}} +}} & {{{Deposition}(i)}} \\{{F\text{-}{change}{\quad }R_{d}L_{4}W_{4}Z_{c}f_{c}} -} & {{V\text{-}{change}}} \\{{{D_{c4}\left( {f_{c} - f_{4}} \right)} -}} & {{{Transference}(4)}} \\{{{D_{c5}\left( {f_{c} - f_{5}} \right)} -}} & {{{Transference}(5)}} \\{{K_{c}V_{c}Z_{c}f_{c}}} & {{Degradation}}\end{matrix} & (51)\end{matrix}$

Also, expressions (42) and (41) in the third embodiment are respectivelyreplaced by: $\begin{matrix}\begin{matrix}{{\frac{f_{5}}{t}V_{5}Z_{5}} = {{\sqrt{D_{c}/t}A_{a5}Z_{5}f_{5}} +}} & {{V\text{-}{change}}} \\{{F\text{-}{change}{\quad }{\gamma_{5}\left( {1 - A_{c}} \right)}\quad \frac{n_{0i}}{L_{zi}}v_{i}V_{i}Z_{i}f_{i}} -} & {{{Deposition}(i)}} \\{{{D_{c5}\left( {f_{5} - f_{c}} \right)} -}} & {{{Transference}(c)}} \\{{{D_{45}\left( {f_{5} - f_{4}} \right)} -}} & {{{Transference}(4)}} \\{{K_{5}V_{5}Z_{5}f_{5}}} & {{Degradation}}\end{matrix} & (52) \\\begin{matrix}{{\frac{f_{4}}{t}V_{4}Z_{4}} = {{{- {GV}_{4}}Z_{4}f_{4}} -}} & {{Ventilation}} \\{{F\text{-}{change}{\quad }{\sum\limits_{{i = 2},8,3}{n_{i}{D_{i4}\left( {f_{4} - f_{i}} \right)}}}} -} & {{{Transference}(i)}} \\{{{\sum\limits_{j = 5}^{7}{D_{4j}\left( {f_{4} - f_{j}} \right)}} -}} & {{{Transference}(j)}} \\{{{K_{4}V_{4}Z_{4}f_{4}} -}} & {{Degradation}} \\{{D_{4c}\left( {f_{4} - f_{c}} \right)}} & {{{Transference}(c)}}\end{matrix} & (53)\end{matrix}$

In expression (52), terms of V-change, Deposition (i), Transference (c),Transference (4), and Degradation respectively indicate the change involume (increase over time) of the carpet fiber, attachment accompanyingthe falling of particles, amount of transference of the compound betweenthe carpet fiber and the space portion, amount of transference of thecompound between the carpet fiber and the air, and change in amount ofphotodegradation of the compound.

In expression (53), terms of Ventilation, Transference (i), Transference(j), Degradation, and Transference (c) respectively indicate the amountof discharge of the compound outdoors, amount of transference of thecompound between the air and the particles, amount of transference ofthe compound between the air and the floor (carpet fiber)/ceiling/wall,change in amount of photodegradation of the compound, and amount oftransference of the compound between the air and the space portion.

Accordingly, Fugacity calculation at S3 is performed such that eightkinds of differential equations of expressions (40), (43), and (44) inthe third embodiment and the above-mentioned expressions (51) to (53)are solved by Runge-Kutta-Gill method. The subsequent steps of S4 to S17are similar to those in the third embodiment.

As explained in the foregoing, in the method of estimating an indoorbehavior of a pesticidal compound in accordance with this embodiment, inthe case where the kind of floor is a carpet having ears of fiber and aspace portion between the ears, a differential equation for Fugacity inthe above-mentioned space portion of the carpet is added to seven kindsof simultaneous differential equations concerning Fugacity in the threekinds of large, medium, and small particles, indoor air, floor (carpetfiber), ceiling, and wall, so as to calculate each Fugacity.

Consequently, even in the case where the chemical is accumulated in thespace portion, so that the compound behaves differently from the casewith a flat floor, the behavior of the compound can be estimatedaccurately, whereby various kinds of simulations can be performed.

(5) Fifth Embodiment

With reference to the drawings, the fifth embodiment of the presentinvention will be explained in the following.

The method of simulating an indoor behavior of a pesticidal compound(hereinafter simply referred to as compound) contained in a chemical(solution) such as insecticide in accordance with this embodimentestimates, for example, the behavior of the compound in the case wherethe chemical is heated to vaporize by use of an electric heatingvaporizer such as electronic mosquito repellent in order to terminateindoor vermin. Here, the chemical encompasses all kinds of insecticidesincluding pyrethroid insecticidal compounds and organophosphorusinsecticidal compounds.

First, as shown in FIG. 15, an environment is classified into 11 kindsof media consisting of 3 kinds of condensed particles 9, 10, and 11,high-concentration air 12, medium-concentration air 13,low-concentration air 14, floor 5, wall 6, high-concentration ceiling15, medium-concentration ceiling 16, and low-concentration ceiling 17.

Namely, in the case where the chemical is vaporized, though the wholecompound is initially evaporated as complete vapor (high-concentrationair 12), the condensed particles 9, 10, and 11 are successively formedwhen the emission rate of the compound (E_(T)) in themedium-concentration air 13 exceeds the saturated amount of the compoundin the vapor. These condensed particles 9, 10, and 11 are divided intothree kinds depending on the time between the occurrence and extinctionof particles. The indoor air other than the above-mentionedhigh-concentration air 12 and medium-concentration air 13, which ismainly respired by humans, is defined as the low-concentration air 14.The high-concentration ceiling 15 is a ceiling portion into which thecondensed particles 9, 10, and 11 are absorbed; the medium-concentrationceiling 16 is a ceiling portion in contact with the medium-concentrationair 13, and the low-concentration ceiling 17 is a ceiling portion incontact with the low-concentration air 14.

Simultaneous differential equations concerning Fugacity of the compoundin the above-mentioned 11 kinds of media are formed and are solved byRunge-Kutta-Gill method, whereby the indoor behavior of the compound inthe chemical when the chemical is heated and vaporized, i.e., temporalchange in compound distribution in the room, is estimated and analyzed.

Here, since the floor 5 mainly comprises three kinds, i.e., tatami,flooring, and carpet (rug), the differential equation is formed so as tocorrespond to the kind of floor. Explained in this embodiment is thecase where the floor 5 is made of tatami.

With reference to FIG. 1, a method of simulating an indoor behavior ofthe compound will be explained. The simulation method in accordance withthis embodiment can be mainly divided into a step of dividing an indoorenvironment into predetermined media and forming a differential equationconcerning a fugacity of the compound in each medium (S1 to S2); a stepof determining the fugacity of the compound in each medium from thedifferential equation (S3); a step of determining the indoor behavior ofthe compound from the fugacity of the compound in each medium (S4); astep of changing, in response to a fluctuation in mass balance of thecompound indoors, a minute time unit used when solving the differentialequation (S21 to S35, see FIG. 5); and a step of evaluating safety ofthe compound with respect to a human body according to the indoorbehavior of the compound (S5 to S17).

First, at step (hereinafter abridged as S) 1, a primary condition isinputted. The primary condition comprises physicochemical properties ofthe compound (see Table 25), indoor environmental behavior properties ofthe compound (see Table 26), indoor environment (see Table 27), andproduct properties (see Table 28).

TABLE 25 PHYSICOCHEMICAL PROPERTY EXAMPLE OF OF COMPOUND SYMBOL VALUEMOLECULAR WEIGHT M_(a) 302.41 [g/mole] SPECIFIC GRAVITY ρ  1.5 × 10⁶[g/m³] VAPOR PRESSURE P^(S) 9.53 × 10^(−3 [Pa]) WATER SOLUBILITY C^(S)1.42 × 10^(−2 [mole/m) ³] OCTANOL/WATER K_(OW)  10^(4.78) DISTRIBUTIONCOEFFICIENT MELTING POINT T_(M) 323 [K]

TABLE 26 INDOOR ENVIRONMENTAL BE- EXAMPLE OF HAVIOR PROPERTY OF COMPOUNDSYMBOL VALUE HALF-LIFE OF DEGRADATION BY LIGHT/OXIDATION IN CONDENSEDPARTICLE τ_(i) (i = 1.08 × 10⁴ [sec] 9,10,11) AIR τ_(j) (j = 12, 1.08 ×10⁴ [sec] 13,14) FLOOR/WALL/CEILING τ_(k) k = 5, 8.64 × 10⁵ [sec]6,15,16, 17) HALF-LIFE OF TRANSFERENCE TO AIR IN FLOOR τ_(jk) (j = 14,3.71 × 10⁵ [sec] k = 5) CEILING τ_(jk) (j = 13, 4.45 × 10⁵ [sec] 14, k =15, 16,17)

TABLE 27 EXAMPLE OF INDOOR ENVIRONMENT SYMBOL VALUE OIL ROOM SIZE V₄23.3 [m^(3]) BASE FLOOR AREA L₄ × W₄  9.7 [m²] TEMPERATURE T 298 [K]RELATIVE HUMIDITY φ 60 [% RH] ABSOLUTE HUMIDITY H 1.19 × 10⁻² [kg-H₂O/kg-dry air] VENTILATION RATE G 0.58 [1/h] INDOOR VAPOR PRESSURE P∞   0[Pa] IN PARTICLE - CONSTI- TUTING SOLUENT AIR DIFFUSION D_(air) 8.64 ×10⁻² COEFFICIENT [m²/h] OIL COMPONENT CONTENT — 0.46 (IN CASE OF TATAMI)0.04 (IN CASE OF FLOORING) 0.04 (IN CASE OF CARPET) WATER WET - BULBTEMPERATURE T_(d) 292.5 [K] BASE VAPOR PRESSURE OF P∞ 1.89 × 10³ [Pa]WATER

TABLE 28 EXAMPLE OF PRODUCT PROPERTY SYMBOL VALUE OIL COMPOUND CONTENTR_(a) 1.94 × 10⁻² [v/v] BASE EMISSION RATE E_(T) 7.36 × 10⁻⁷ [g/ sec]CONDENSATION RATIO C_(r) 0.98 PARTICLE-CONSTITUTING SOLVENT PROPERTYVAPOR PRESSURE P_(d) 1.77 [Pa] MOLECULAR WEIGHT M_(d) 198.39 [g/mole]SPECIFIC GRAVITY ρ_(d) 7.56 × 10⁵ [g/m³] DIAMETER OF CONDENSED PARTICLEd₀  3.5 [μm] VOLUME OF HIGH - CONCENTRATION AIR V₁₂   2 [m^(3]) VOLUMEOF MEDIUM - CONCENTRATION AIR V₁₃   3 [m^(3]) VOLUME OF LOW -CONCENTRATION AIR V₁₄ 18.3 [m^(3]) CROSS - SECTIONAL AREA OF HIGH -CONCENTRATION AIR A₁₂  1.2 [m^(2]) CROSS - SECTIONAL AREA OF MEDIUM -A₁₃ 0.96 [m^(2]) CONCENTRATION AIR CROSS - SECTIONAL AREA OF LOW -CONCENTRATION AIR A₁₄ 7.48 [m^(2]) WATER PARTICLE-CONSTITUTING SOLVENTPROPERTY BASE VAPOR PRESSURE P_(d) 2.26 × 10³ [Pa] MOLECULAR WEIGHTM_(d)   18 [g/mole] SPECIFIC GRAVITY ρ_(d)   1 × 10⁶ [g/m³]

Here, A₁₂, A₁₃, and A₁₄ in Table 28 indicate cross-sectional areas ofthe respective airs 12, 13, and 14 with respect to the direction ofmovement of indoor air (arrow in FIG. 15).

The examples of values in Tables 25 to 28 assume those of a six-mat room(9.72 [m²]) of a typical apartment in Japan in summer, using an electricheating vaporizer employing an oil-based chemical (see FIGS. 16A and16B). The electric heating vaporizer comprises a core portion of 1[cm]×1 [cm] (at a temperature of 405 [K]), a heater portion of 4 [cm]×4[cm]×0.5 [cm] (at a temperature of 373 [K]), and a container in which achemical is packed (at a temperature of 303 [K]). The example of valueof compound content (R_(a)) in Table 28 indicates the volume of compoundrelative to the volume of particles immediately after condensation.

Subsequently, using the primary condition, a secondary condition isdetermined by calculation (S2). The secondary condition comprises atemporally unchangeable definite factor condition (see Table 29)determined by the primary condition alone and a temporal changecondition accompanying a temporal change (see Table 30). Theircalculations will be explained later in detail.

TABLE 29 DEFINITE FACTOR CONDITION SYMBOL FLOATING NUMBER OF CONDENSEDn_(i) (i = 9,10,11) PARTICLES EVAPORATION CONSTANT OF α CONDENSEDPARTICLES EMISSION AMOUNT OF CHEMICAL IN E_(v) GAS STATE DIFFUSIONCOEFFICIENT OF COMPOUND D_(ca) IN AIR SURFACE AREA OF FLOOR/WALL/CEILINGA_(k) (k = 5,6,15,16,17) DIFFUSION COEFFICIENT OF FLOOR/ D_(c)WALL/CEILING AIR VELOCITY V_(f) FUGACITY CAPACITY OF CONDENSED PARTICLEZ_(i) (i = 9,10,11) AIR Z_(j) (j = 12,13,14) FLOOR/WALL/CEILING Z_(k) (k= 5,6,15,16,17) DEGRADATION CONSTANT OF CONDENSED PARTICLE K_(i) (i =9,10,11) AIR K_(j) (j = 12,13,14) FLOOR/WALL/CEILING K_(k) (k =5,6,15,16,17)

TABLE 30 TEMPORAL CHANGE CONDITION SYMBOL CONDENSED PARTICLE DIAMETERd_(i) (i = 9,10,11) TRANSFERENCE SPEED OF COMPOUND IN CONDENSED PARTICLEk_(i) (i = 9,10,11) AIR k_(j) (j = 12,13,14) FLOOR/WALL/CEILING k_(k) (k= 5,6,15,16,17) TRANSFERENCE COEFFICIENT OF D_(i13 (i = 9,10,11))COMPOUND BETWEEN CONDENSED PARTICLE AND AIR TRANSFERENCE COEFFICIENT OFD_(jk) (j = 12,13,14, COMPOUND BETWEEN AIR AND k = 5,6,15,16,17)FLOOR/WALL/CEILING VOLUME OF CONDENSED PARTICLE V_(i) (i = 9,10,11)VOLUME OF FLOOR/WALL/CEILING V_(k) (k = 5,6,15,16,17)

Using the secondary condition, 11 kinds of Fugacity are calculated (S3).Namely, 11 kinds of differential equations concerning the 3 kinds ofcondensed particles 9, 10, and 11, 3 kinds of air 12, 13, and 14, floor5, wall 6, and 3 kinds of ceilings 15, 16, and 17 are simultaneouslyformed and are solved by Runge-Kutta-Gill method, whereby 11 kinds ofFugacity are computed over time. Here, an estimation nick time width(minute time unit) set when solving the differential equations isautomatically set so as to be varied in response to a fluctuation inmass balance of the compound.

At S4, using thus computed Fugacity (f₁₄) of the low-concentration air14, temporal concentration of the compound in the air is computed;whereas temporal residual amounts of the compound on the floor 5 iscomputed by use of Fugacity (f₅) of the floor 5.

At S5, it is judged whether or not to perform safety evaluation in thecase where the chemical is inhaled. If the safety evaluation ininhalation is to be performed, then an estimated exposure amount ininhalation indicating a degree of exposure upon inhalation of thecontaminated air is computed by use of the above-mentioned temporalconcentration in the indoor air (S6). Thereafter, an inhalation safetycoefficient is computed according to the estimated exposure amount ininhalation (S7). At S8, the inhalation safety coefficient is comparedwith a reference value defined in each country. If the inhalation safetycoefficient exceeds the reference value, it is judged that “there is noproblem in safety.” By contrast, if the inhalation safety coefficient islower than the reference value at S8, it is judged that “there is aproblem in safety”, and the operation returns to S1, where alteration ofthe primary condition such as alteration of compound, alteration ofchemical formulation, alternation of using condition, or the like isconsidered.

If the safety evaluation in inhalation is not selected at S5, calculatedis an estimated amount of percutaneous exposure indicating to whatextent the skin is exposed in contact with the floor 5 to which thechemical is attached (S9). Thereafter, at S10, it is judged whether toperform a percutaneous safety evaluation or not. If the percutaneoussafety evaluation is to be performed, a percutaneous safety coefficientis computed according to the estimated percutaneous exposure amount(S11). At S12, as with the safety evaluation in inhalation, thepercutaneous safety coefficient is compared with a reference valuedefined in each country, whereby the safety is evaluated. If there is aproblem in safety at S12, the operation returns to S1, where alterationof the primary condition is considered.

If the percutaneous safety evaluation is not selected at S10, calculatedat S13 according to the estimated percutaneous exposure amount is anestimated oral exposure amount indicating the degree of exposure in thecase where the chemical attached to a hand or the like is taken orally(S13). Subsequently, according to the estimated oral exposure amount, anoral safety coefficient is computed (S14). This oral exposure may occur,in particular, when an infant puts a chemical-attached hand into themouth. At S15, as with the safety evaluation in inhalation, the oralsafety coefficient is compared with a reference value defined in eachcountry, whereby the safety is evaluated. If there is a problem insafety at S15, the operation returns to S1, where alteration of theprimary condition is considered.

Finally, if it is judged to be safe at S8, S12, or S15, overall safetyis evaluated. Here, the sum of respective reciprocals of the previouslydetermined inhalation safety coefficient, percutaneous safetycoefficient, and oral safety coefficient is determined, and thereciprocal of thus determined value is defined as an overall safetycoefficient (S16). This overall safety coefficient is compared with areference value, whereby an evaluation similar to the previous safetyevaluation is effected (S17).

In the following, the above-mentioned steps of S2 to S4, S6, S7, S9,S11, S13, and S14 will be explained in detail.

(i) Secondary Condition Calculation (S2)

Calculations of the definite factor condition shown in Table 29 and thetemporal change condition shown in Table 30 will be explained.

The condensed particles 9, 10, and 11 are successively generated duringtime t₁ and are absorbed by the high-concentration ceiling 15.Specifically, the condensed particles 9 exist during the period of timet₁/3 after evaporation, the condensed particles 10 are generated afterthe lapse of time t₁/3, and the condensed particles 11 are generatedafter the lapse of time 2t₁/3. Here, the floating number (n_(i), i=9,10, 11) of the condensed particles is constant from their generationtill absorption, and is expressed, from the specific gravity (ρ) of thecompound, compound content (R_(a)), emission rate (E_(T)), condensationratio (C_(r)), and initial diameter (d₀) of condensed particles 9, 10,and 11, as follows: $\begin{matrix}\left. \begin{matrix}{n_{i} = {\left( \frac{n_{T}}{t} \right)\quad \frac{t_{1}}{3}}} \\{\frac{n_{T}}{t} = {{E_{T}{C_{r}/\left( {\frac{\pi}{6}d_{0}^{3}R_{a}\rho} \right)}} - G}}\end{matrix} \right\} & (54)\end{matrix}$

wherein G is the ventilation rate.

According to surface temperature (T_(d)) of particles, properties ofparticle-constituting solvent (vapor pressure P_(d), molecular weightM_(d), and specific gravity ρ_(d)), and indoor environment (airdiffusion coefficient D_(air), vapor pressure P^(∞), and roomtemperature T^(∞)), the evaporation constant (α) of the condensedparticles 9, 10, and 11 is defined as follows: $\begin{matrix}{\alpha = {\frac{4D_{air}M_{d}}{R\quad \rho_{d}}\left( {\frac{P_{d}}{T_{d}} - \frac{P\quad \infty}{T\quad \infty}} \right)}} & (55)\end{matrix}$

wherein R is a gas constant.

Here, the upper parts of the above-mentioned Tables 27 and 28 exemplifythe case where the heat-vaporized aerosol is of oil base. In this case,T^(∞) (temperature at the site far from particles) and T_(d) are set toroom temperature (T), whereas P^(∞) (vapor pressure of oil at the sitefar from particles) is set to zero.

In the case where the heat-vaporized aerosol is of water base, it isnecessary for P_(d), M_(d), ρ_(d), T_(d), and P^(∞) in expression (55)to be changed to values based on properties of water. Specifically, theabove-mentioned factor values when the room temperature (T) is 298 [K](=25° C.) and the relative humidity is 60[% RH] are exemplified in thelower parts of Tables 27 and 28.

Here, T_(d) can be determined, according to the room temperature (T) andrelative humidity (H), from “mass-based humidity table” disclosed in“Kagaku Kikai no Riron to Keisan (Theory and Calculation of ChemicalMachines)” (Second Edition) (Saburo Kamei ed., Sangyo Tosho) or thelike. On the other hand, P_(d) and P^(∞) can be computed from thefollowing expressions:

log₁₀ P _(d)=10.23−1750/(T _(d)−38)

log₁₀ P ^(∞)=8.23−1750/(T−38)+log₁₀ψ

wherein ψ is an indoor relative humidity.

From the molecular weight (M_(a)) of the compound, emission rate(E_(T)), and condensation rate (C_(r)), the amount of emission ofchemical (E_(v)) to the high-concentration air 12 is expressed asfollows:

E _(v) =E _(T)(1−C _(r))/M _(a)  (56)

The surface area (A_(k), k=5, 6, 15, 16, 17) of each of the floor 5,wall 6, high-concentration ceiling 15, medium-concentration ceiling 16,and low-concentration ceiling 17 is determined by the room size (V₄) andfloor area (L₄×W₄).

Using the room size (V₄), ventilation rate (G), and cross-sectional area(A₁₄) of the room with respect to the direction of movement of indoorair, the indoor air velocity (V_(f)) is determined as follows:$\begin{matrix}{V_{f} = {G\frac{V_{4}}{A_{14}}}} & (57)\end{matrix}$

From the vapor pressure (P^(s)) and melting point (T_(M)) of thecompound and surface temperature (T_(d)) of particles, Fugacity capacity(Z_(i), i=9, 10, 11) of the condensed particles 9, 10, and 11 isexpressed as: $\begin{matrix}{{Z_{i} = \frac{6 \times 10^{6}}{P_{L}^{s}{RT}_{d}}}{P_{L}^{s} = {P^{s}\exp \left\{ {6.79\left( {{T_{M}/T_{d}} - 1} \right)} \right\}}}} & (58)\end{matrix}$

Though the vapor pressure of the compound in a liquid state (P_(L) ^(s))is computed by use of T_(M) and T_(d) here; in the case where T_(M)cannot be obtained, P_(L) ^(s) may be set identical to the vaporpressure of the compound in a solid state (P^(s)).

From the room temperature (T), Fugacity capacity (Z_(j), j=12, 13, 14)of the airs 12, 13, and 14 is expressed as follows: $\begin{matrix}{Z_{j} \simeq \frac{1}{RT}} & (59)\end{matrix}$

From the vapor pressure (P^(s)), water solubility (C^(s)), andoctanol/water distribution coefficient (K_(ow)) of the compound, andfrom the oil component content (ρ_(k), k=5, 6, 15, 16, 17) of thematerial constituting the floor 5, wall 6, and ceilings 15, 16, and 17,Fugacity capacity (Z_(k), k=5, 6, 15, 16, 17) of the floor 5, wall 6,and ceilings 15, 16, and 17 is expressed as:

Z _(k)=ρ_(k) K _(OW) C ^(s) /P ^(s)  (60)

Mainly generated in the 11 kinds of media are degradation reactionscaused by light and oxidation. The degradation constant (K_(i), i=9, 10,11) of the condensed particles 9, 10, and 11, degradation constant(K_(j), j=12, 13, 14) of the airs 12, 13, and 14, and degradationconstant (K_(k), k=5, 6, 15, 16, 17) of the floor 5, wall 6, andceilings 15, 16, and 17 are defined by use of the respective half-livesof degradation by light/oxidation (τ_(i)), (τ_(j)), and (τ_(k)).$\begin{matrix}\left. \begin{matrix}{K_{i} = \frac{0.693}{\tau_{i}}} \\{K_{j} = \frac{0.693}{\tau_{j}}} \\{K_{k} = \frac{0.693}{\tau_{k}}}\end{matrix} \right\} & (61)\end{matrix}$

While τ_(i) and τ_(k) are often unavailable, K_(i) and K_(k) may benullified in this case from the viewpoint of securing safety ofinhabitants. When τ_(j) of the compound in the air is unavailable, itmay be determined by use of Atmospheric Oxidation program (Atkinson etal., 1984, Chem. Rev. Vol. 84, pp. 437-470) from the structural formulaof the compound.

Since the volume of particles decreases over time due to evaporation ofthe particle-constituting solvent component, during the evaporation ofparticle-constituting solvent component, using the diameter (d₀) ofparticles immediately after spraying (t=0) and the evaporation constant(α) determined from expression (55), the diameter (d_(i), i=9, 10, 11)of the condensed particles 9, 10, and 11 at time t is represented as:

d _(i) ={square root over (d₀ ²−2αt)}  (62)

From the diameter (d_(i)) of condensed particles 9, 10, and 11determined by expression (62), indoor velocity (v_(f)) determined byexpression (57), and Fugacity capacity (Z_(i)) of condensed particles 9,10, and 11 determined by expression (58), and Fugacity capacity (Z₁₃) ofthe medium-concentration air 13 determined by expression (59), thetransference coefficient (D_(i13)) between the condensed particles 9,10, and 11 and the medium-concentration air 13 becomes: $\begin{matrix}{D_{i13} = \frac{1}{{1/\left( {k_{i}A_{i}Z_{i}} \right)} + {1/\left( {k_{13}A_{i}Z_{13}} \right)}}} & (63)\end{matrix}$

wherein A_(i) (=πd_(i) ²) is the surface area of particles, k₁₃(=v_(f)+v_(i)) is the transference speed of the compound in themedium-concentration air 13, and k_(i) (=v_(f)/100) is the transferencespeed of the compound in the particles. Here, v_(i) is the floatingspeed of the condensed particles 9, 10, and 11, and can be determined byuse of hydrodynamics since it is under the control of the flow caused bythe heat of the electric heating vaporizer, gravity, and air resistance.

From the half-life of transference to air (τ_(jk)) in the ceilings 15,16, and 17, volume (V_(j), j=12, 13, 14) of the airs 12, 13, and 14,volume (V_(k)) of the floor/wall/ceiling determined by expression (66)mentioned later, Fugacity capacity (Z_(j)) of airs 12, 13, and 14determined by expression (59), and Fugacity capacity (Z_(k)) offloor/wall/ceiling determined by expression (60), the transferencecoefficient (D_(jk)) of the compound between the medium-concentrationair 13 and the ceilings 15 and 16 or between the low-concentration air14 and the floor 5, wall 6, and low-concentration ceiling 17 becomes:$\begin{matrix}{D_{jk} = \frac{0.693}{\tau_{jk}\left\{ {{1/\left( {V_{j}Z_{j}} \right)} + {1/\left( {V_{k}Z_{k}} \right)}} \right\}}} & (64) \\{D_{jk} = \frac{1}{{1/\left( {k_{j}A_{jk}Z_{j}} \right)} + {1/\left( {k_{k}A_{jk}Z_{k}} \right)}}} & \left( 64^{\prime} \right)\end{matrix}$

Here, the total volume V₁₂+V₁₃+V₁₄ of the airs 12, 13, and 14 equals thevolume (V₄) of the room.

The above-mentioned transference coefficient (D_(jk)) may also bedetermined by the expression represented by the above-mentionedexpression (64′) by use of the transference speed (k_(j)) of thecompound in the air and the transference speed (k_(k)) of the compoundin the interior materials (floor 5, wall 6, and ceilings 15, 16, and17).

Here, the half-life of transference to air (τ_(jk)) in expression (64)is hard to actually measure and varies under various conditions, thusmaking it difficult to determine an accurate value thereof. By contrast,all the parameters in expression (64′) can be easily determined bycalculation without necessitating measurement. For example, using thediffusion coefficient (D_(c)) of compound, the transference speed(k_(k)) of the compound in the interior material is calculated as(D_(c)/t)^(0.5); whereas A_(jk) can be determined from the contact areabetween the individual airs 12, 13, and 14 and the individual interiormaterials (floor 5, wall 6, and ceilings 15, 16, and 17). Here, D_(c)can be determined when the diffusion coefficient (D_(ca)) of thecompound in the air is multiplied by 10⁻⁹, whereas D_(ca) can becomputed from properties of the compound (e.g., structural formula,molecular weight, and the like) according to Wike and Lee method(“Handbook of Chemical Property Estimation Methods,” McGraw-Hill BookCompany, 1982), for example. Accordingly, the transference coefficient(D_(jk)) is more preferably determined by expression (64′) than byexpression (64).

Using the diameter (d_(i)) of particles determined by expression (62)and the evaporation constant (α), change in volume (dv_(i)/dt) of thecondensed particles 9, 10, and 11 is expressed by: $\begin{matrix}{\frac{V_{i}}{t} = {{- \frac{\pi}{2}}\alpha \quad d_{i}}} & (65)\end{matrix}$

Namely, as the particle-constituting solvent component evaporates overtime, the volume (V_(i), i=9, 10, 11) of condensed particles 9, 10, and11 decreases.

Assuming that each of the floor 5, wall 6, and ceilings 15, 16, and 17before heat-vaporizing the chemical is like a thin film and that, as thechemical infiltrates into the film, its thickness increases so as toenhance the volume thereof; from the surface area (A_(k)) of thefloor/wall/ceiling and diffusion coefficient (D_(c)) of the compound inthe floor/wall/ceiling, the volume (V_(k), k=5, 6, 15, 16, 17) offloor/wall/ceiling becomes:

V _(k)=2{square root over (D_(c)t)} A _(k)  (66)

(ii) Fugacity Calculation (S3)

The behavior of the compound in the condensed particles 9, 10, and 11 isexpressed in the form of differential equation concerning Fugacity(f_(i)) as: $\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{i}}{t}V_{i}Z_{i}} = {\underset{V\text{-}{change}}{\frac{\pi}{2}\alpha \quad d_{i}Z_{i}f_{i}} - \underset{{Transference}(13)}{D_{i13}\left( {f_{i} - f_{13}} \right)} - \underset{Degradation}{K_{i}V_{i}Z_{i}f_{i}}}} & (67)\end{matrix}$

Here, the terms of V-change, Transference (13), and Degradationrespectively indicate the volume change (decrease over time) of thecondensed particles, amount of transference of the compound between thecondensed particles 9, 10, and 11 and the medium-concentration air 13,and amount of degradation of the compound by light and oxidation in thecondensed particles 9, 10, and 11 (K_(i)V_(i)Z_(i) indicating thedegradation speed quantity). Here, when the condensed particles 9, 10,and 11 are absorbed by the high-concentration ceiling 15, Fugacity(f_(i)) immediately disappears and is added to Fugacity (f₁₅) explainedlater.

The behavior of the compound in the high-concentration air 12 isexpressed in the form of differential equation concerning Fugacity (f₁₂)as: $\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{12}}{t}V_{12}Z_{12}} = {\underset{{Emission}\quad {{Transference}(f)}}{E_{v} + {v_{f}{A_{12}\left( {{Z_{13}f_{13}} - {Z_{12}f_{12}}} \right)}}} - \underset{Degradation}{K_{12}V_{12}Z_{12}f_{12}}}} & (68)\end{matrix}$

Here, the terms of Emission, Transference (j), and Degradationrespectively indicate the amount of emission of the compound as completevapor, amount of transference of the compound with respect to themedium-concentration air 13, and amount of degradation of the compoundby light and oxidation (K₁₂V₁₂Z₁₂ indicating the degradation speedquantity).

The behavior of the compound in the medium-concentration air 13 isexpressed in the form of differential equation concerning Fugacity (f₁₃)as: $\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{13}}{t}V_{13}Z_{13}} = {{v_{f}\underset{\quad {{Transference}(j)}}{\left\{ {{A_{12}Z_{12}f_{12}} - {\left( {A_{12} + A_{13}} \right)Z_{13}f_{13}} + {A_{13}Z_{14}f_{14}}} \right\}}} - \underset{{Transference}(i)}{\sum\limits_{i = 9}^{11}{n_{i}{D_{i13}\left( {f_{13} - f_{i}} \right)}}} - \underset{{Transference}(k)}{\sum\limits_{k = 15}^{16}{D_{13k}\left( {f_{13} - f_{k}} \right)}} - \underset{Degradation}{K_{13}V_{13}Z_{13}f_{13}}}} & (69)\end{matrix}$

Here, the terms of Transference (j), Transference (i), Transference (k),and Degradation respectively indicate the amount of transference of thecompound with respect to the high-concentration air 12 andlow-concentration air 14, amount of transference of the compound withrespect to the condensed particles 9, 10, and 11, amount of transferenceof the compound with respect to the ceilings 15 and 16, and amount ofdegradation of the compound by light and oxidation (K₁₃V₁₃Z₁₃ indicatingthe degradation speed quantity).

The behavior of the compound in the low-concentration air 14 isexpressed in the form of differential equation concerning Fugacity (f₁₄)as: $\begin{matrix}\begin{matrix}{\left. {\underset{F\text{-}{change}}{\frac{f_{14}}{t}V_{14}Z_{14}} = {\underset{{Transference}(j)}{v_{f}\left\{ {A_{13}Z_{13}f_{13}} \right.} - \underset{\&\quad {Ventilation}}{\left( {A_{13} + A_{14}} \right)Z_{14}f_{14}}}} \right\} -} \\{{\underset{{Transference}(k)}{\sum\limits_{k = 5}^{6}{D_{14k}\left( {f_{14} - f_{k}} \right)}} - \underset{{Transference}(17)}{{D_{1417}\left( {f_{14} - f_{17\quad}} \right)} -}}} \\{\underset{Degradation}{K_{14}V_{14}Z_{14}f_{14}}}\end{matrix} & (70)\end{matrix}$

Here, the terms of Transference (j) & Ventilation, Transference (k),Transference (17), and Degradation respectively indicate the amount oftransference of the compound with respect to the medium-concentrationair 13 and the amount of discharge thereof outdoors, amount oftransference of the compound with respect to the floor 5 and wall 6,amount of transference of the compound with respect to thelow-concentration ceiling 17, and amount of degradation of the compoundby light and oxidation (K₁₄V₁₄Z₁₄ indicating the degradation speedquantity).

The behaviors of the compound in the floor 5 and wall 6 are respectivelyexpressed in the forms of differential equations concerning Fugacity(f₅) and (f₆) as follows: $\begin{matrix}\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{5}}{t}V_{5}Z_{5}} = {\underset{V\text{-}{change}}{{- \sqrt{D_{c}/t}}\quad A_{5}Z_{5}f_{5}}\underset{{Transference}(14)}{{{- D_{145}}\left( {f_{5} - f_{14}} \right)} -}}} \\{\underset{Degradation}{K_{5}V_{5}Z_{5}f_{5}}}\end{matrix} & (71) \\\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{6}}{t}V_{6}Z_{6}} = {\underset{V\text{-}{change}}{{- \sqrt{D_{c}/t}}\quad A_{6}Z_{6}f_{6}}\underset{{Transference}(14)}{{{- D_{146}}\left( {f_{6} - f_{14}} \right)} -}}} \\{\underset{Degradation}{K_{6}V_{6}Z_{6}f_{6}}}\end{matrix} & (72)\end{matrix}$

Here, in each expression, the terms of V-change, Transference (14), andDegradation respectively indicate the volume change (increase over time)of the floor 5 or wall 6, amount of transference of the compound withrespect to the floor 5 or wall 6, and amount of degradation of thecompound by light and oxidation (K₅V₅Z₅ or K₆V₆Z₆ indicating thedegradation speed quantity).

The behaviors of the compound in the high-concentration ceiling 15,medium-concentration ceiling 16, and low-concentration ceiling 17 arerespectively expressed in the forms of differential equations concerningFugacity (f₁₅), (f₁₆), and (f₁₇) as follows: $\begin{matrix}\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{15}}{t}V_{15}Z_{15}} = {\underset{V\text{-}{change}}{{- \sqrt{D_{c}/t}}\quad A_{15}Z_{15}f_{15}}\underset{{Transference}(13)}{{{- D_{13\quad 15}}\left( {f_{15} - f_{13}} \right)} -}}} \\{\underset{Degradation}{K_{15}V_{15}Z_{15}f_{15}}}\end{matrix} & (73) \\\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{16}}{t}V_{16}Z_{16}} = {\underset{V\text{-}{change}}{{- \sqrt{D_{c}/t}}\quad A_{16}Z_{16}f_{16}}\underset{{Transference}(13)}{{{- D_{13\quad 16}}\left( {f_{16} - f_{13}} \right)} -}}} \\{\underset{Degradation}{K_{16}V_{16}Z_{16}f_{16}}}\end{matrix} & (74) \\\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{17}}{t}V_{17}Z_{17}} = {\underset{V\text{-}{change}}{{- \sqrt{D_{c}/t}}\quad A_{17}Z_{17}f_{17}}\underset{{Transference}(14)}{{{- D_{14\quad 17}}\left( {f_{17} - f_{14}} \right)} -}}} \\{\underset{Degradation}{K_{17}V_{17}Z_{17}f_{17}}}\end{matrix} & (75)\end{matrix}$

Here, in each expression, the terms of V-change, Transference (13),Transference (14), and Degradation respectively indicate the volumechange (increase over time) of the ceilings 15, 16, and 17, amount oftransference of the compound between the high-concentration ceiling 15or medium-concentration ceiling 16 and the medium-concentration air 13,amount of transference of the compound between the low-concentrationceiling 17 and the low-concentration air 14, and amount of degradationof the compound by light and oxidation (K₁₅V₁₅Z₁₅, K₁₆V₁₆Z₁₆, orK₁₇V₁₇Z₁₇ indicating the degradation speed quantity).

When the following Fugacity (f_(a)) is added to the floor (k=5), wall(k=6), and ceiling (k=15, 16, 17) by a predetermined ratio, accuracy canbe improved.

f _(a) =n _(i) V _(tia) Z _(i) f _(ia) /V _(k) /Z _(k)  (76)

Here, V_(tia) and f_(ia) respectively indicate the volume and Fugacityof particles immediately before the condensed particles attach to theinterior materials.

The above-mentioned 11 kinds of differential equations (67) to (75) aresimultaneously formed and are solved by Runge-Kutta-Gill method, so asto compute Fugacity (f₅, f₆, f₉ to f₁₇).

When solving these simultaneous differential equations, it is necessaryto set an estimation nick time width (dt) which is a minute time unit.Namely, the estimation nick time width is used such that solutions ofthe simultaneous differential equations are initially determined at atime (t₀), and then solutions of the simultaneous differential equationsare determined at a time (t₀+dt) to which the estimation nick time widthis added. As solutions are obtained while estimation nick time widthsare successively added, temporally changing Fugacity can be determined.Theoretically, as the set time of the estimation nick time width isshorter, more accurate solutions can be obtained, though necessitating avery long calculation time. By contrast, when the set time is too long,solutions tend to diverge, thereby generating errors.

Therefore, in the present invention, the estimation nick time width isset shorter when a very large change occurs in a chemical, whereas it isset longer when there is no large change.

Specifically, mass balance is always confirmed such that the amount ofinput of the chemical and the resulting solution coincide with eachother, and the estimation nick time width is set longer when the massbalance does not fluctuate greatly, whereas it is set shorter when themass balance starts fluctuating. For example, when the fluctuation ofmass balance is set to an accuracy of ±5%, the estimation nick timewidth is always set so as to constantly satisfy the relationship of:

compound input amount/(existing amount+degrading amount+dischargingamount)=0.95 to 1.05

namely, such that the fluctuation of mass balance lies within the rangeof ±5%.

Here, the above-mentioned compound input amount is determined by thecompound content (R_(a)) and emission rate (E_(T)). Since the temporalamounts of compound in the 11 kinds of media are determined by thesimultaneous differential equations, they are summed up so as to computethe existing amount as shown in the following: $\begin{matrix}\left. \begin{matrix}\begin{matrix}\begin{matrix}{{{existing}\quad {amount}} = {{\sum\limits_{i = 9}^{11}{n_{i}V_{i}Z_{i}f_{i}}} + {\sum\limits_{k = 5}^{6}{f_{k}V_{k}Z_{k}}} + {\sum\limits_{k = 12}^{17}{f_{k}V_{k}Z_{k}}}}} \\{{{degrading}\quad {amount}} = {{\sum\limits_{i = 9}^{11}{n_{i}K_{i}V_{i}Z_{i}f_{i}}} + {\sum\limits_{k = 5}^{6}{K_{k}f_{k}V_{k}Z_{k}}} +}}\end{matrix} \\{\sum\limits_{k = 12}^{17}{K_{k}f_{k}V_{k}Z_{k}}}\end{matrix} \\{{{discharging}\quad {amount}} = {v_{f}A_{14}Z_{14}f_{14}}}\end{matrix} \right\} & (77)\end{matrix}$

The degrading amount and discharging amount are as represented above.

With reference to the flowchart of FIG. 5, the method of setting theestimation nick time width (dt) will be explained.

First, an initial value of estimation nick time width (dt) is inputted(S21). Then, an upper limit set value (e.g., 0.1[%]) which is the upperlimit of difference in mass balance, and a lower limit set value (e.g.,10⁻⁶[%]) which is the lower limit of difference in mass balance areinputted (S22). Thereafter, Fugacity and mass balance at t=t₀ arecalculated (S23 and S24), and Fugacity and mass balance at t=t+dt (ort₀+dt) are calculated (S25 and S26).

It is judged whether the fluctuation in mass balance is within the rangeof ±5% or not (S27). If the fluctuation in mass balance is within therange of ±5%, it is judged whether the difference between the massbalance at t=t (or t₀) and the mass balance at t=t+dt (or t₀+dt) is atleast the upper limit set value or not (S28). If it is judged to be atleast the upper limit set value at S28, then solutions become moreaccurate when the estimation nick time width (dt) is made shorter. Inthis case, the estimation nick time width (dt) is multiplied by ½ so asto change its setting (S29). When the difference is judged to be smallerthan the upper limit set value at S28, it is judged at S30 whether thedifference between the mass balance at t=t (or t₀) and the mass balanceat t=t+dt (or t₀+dt) is at most the lower limit set value or not.

When the mass balance difference is not greater than the lower limit setvalue at S30, since solutions are not influenced by longer estimationnick time width (dt), the estimation nick time width (dt) is doubled soas to change its setting (S31). Subsequently, it is judged whether theestimation nick time width (dt) changed at S31 is at most a maximumvalue (e.g., 0.1 [hour]) of estimation nick time width (dt) or not(S32). When the estimation nick time width (dt) is not greater than themaximum value at S32, since solutions do not diverge, the estimationnick time width (dt) set at S31 is used. When the estimation nick timewidth (dt) is greater than the maximum value at S32, since solutions maydiverge, the estimation nick time width (dt) is reset to the maximumvalue (S33). When the mass balance difference is greater than the lowerlimit set value at the above-mentioned S30, namely, when it lies betweenthe lower limit set value and upper limit set value, the calculationsare continued without changing the estimation nick time width (dt).

After the step of S29, S30, S32, or S33, the operation returns to S25 soas to effect calculation again, and this process is repeated till theaimed time is attained.

When the fluctuation in mass balance exceeds the range of ±5% at S27, onthe other hand, the mass balance fluctuation is so much that calculationis preferably effected with an estimation nick time width (dt) shorterthan that in the case where the fluctuation is within the range of ±5%.Accordingly, the calculation is stopped once (S34), the lower limit setvalue is reset to a lower level (S35), and then the operation returns tothe step of S23.

Thus, when the estimation nick time width is variably set without beingheld constant, while monitoring the mass balance fluctuation, Fugacitycan be computed accurately and efficiently.

(iii) Computation of Temporal Concentration in Indoor Air and FloorResidual Amount (S4)

The temporal concentration of the compound in the indoor air is computedwhen Fugacity (f₁₄) of the low-concentration air 14, determined by theabove-mentioned item(ii), is multiplied by its Fugacity capacity (Z₁₄).The concentration in the low-concentration air 14 is used because themost part in the room is filled with the low-concentration air 14, andhumans are most likely to inhale the low-concentration air 14. Theconcentration in the air of other concentrations may also be used whennecessary.

The floor residual amount of the compound is computed when Fugacity (f₅)of the floor is multiplied by Fugacity capacity (Z₅).

(iv) calculation of Estimated Exposure Amount in Inhalation andInhalation Safety Coefficient (S6 and S7)

The above-mentioned temporal concentration in the indoor air forms acurve shown in FIG. 3A, for example. This concentration curve isintegrated, an accumulated concentration of the compound during aspecific period (t₁ to t₂) is determined (see FIG. 3B), and the meanconcentration in the indoor air is computed from thus determined value.While an arbitrary period is set as the specific period depending on theobject, an appropriate period is usually set in view of the method ofuse of the product and the test period of toxicity data.

Then, according to the above-mentioned mean concentration in the indoorair, amount of respiration, and exposure time, the estimated exposureamount in inhalation is determined. Namely, calculation of:

estimated exposure amount in inhalation [mg/kg/day]=mean concentrationin indoor air [mg/m³]×amount of respiration [m³/kg/min]×exposure time[min/day]

is effected. Here, as the above-mentioned amount of respiration, apublished value or actually measured value may be used. Also, whenamounts of respiration are respectively set for adult and child, moreappropriate estimated exposure amounts in inhalation can be obtained. Inthe case where the inhaled harmful material is not totally absorbed intothe body but is partially discharged by respiration, a more appropriateestimated exposure amount in inhalation can be obtained when theinhalation ratio is taken into account.

The inhalation safety coefficient is computed from a non-influentialamount concerning inhalation toxicity examined by an animal experimentbeforehand and the estimated exposure amount in inhalation determinedabove. Namely, it is expressed as:

inhalation safety coefficient=inhalation non-influential amount[mg/kg/day]/estimated exposure amount in inhalation [mg/kg/day]

(v) Calculation of Estimated Percutaneous Exposure Amount andPercutaneous Safety Coefficient (S9 and S11)

The above-mentioned floor residual amount forms a curve such as thatshown in FIG. 4A, for example. This residual amount curve is integrated,the accumulated residual amount of the compound during a specific period(t₁ to t₂) is determined (see FIG. 4B), and the mean residual amount iscomputed from thus determined value. While an arbitrary period is set asthe specific period depending on the object, an appropriate period isusually set in view of the method of use of the product and the testperiod of toxicity data.

Then, according to the mean floor residual amount, skin attachmentratio, contact area, and body weight, the estimated percutaneousexposure amount is determined. Namely, calculation of:

estimated percutaneous exposure amount [mg/kg/day]=(mean residual amount[mg/m²]×skin attachment ratio [%]×contact area [m²/day])/body weight[kg]

is effected. Here, as the contact area, a published value (e.g., 4[m²/day]) may be used. The skin attachment ratio is a ratio of thecompound attaching to the skin when the latter is in contact with thefloor 5 where the compound exists. As this value, a published value or avalue experimentally obtained from a model may be used.

A model experiment method for the skin attachment ratio is as follows. Aweight (8 cm×8 cm×8 cm; 4.2 kg) is placed on a denim cloth (8 cm×10 cm)with a pressure similar to that of an infant in contact with a floor,and the denim cloth is pulled on the floor at a speed (120 cm/15 sec)similar to the moving speed of the infant. The denim and floor areanalyzed so as to compute the compound contained in the denim and floor.From the ratio therebetween, the skin attachment ratio is obtained. Ithas been confirmed that the skin attachment ratio obtained by thismethod is identical to or slightly higher than that determined fromanalyzed values of a hand and a floor when the hand is actually pressedagainst the floor, thereby proving this model experiment method to beuseful for evaluating exposure of inhabitants.

The percutaneous safety coefficient is computed from the non-influentialamount concerning percutaneous toxicity examined by an animal experimentbeforehand and the estimated percutaneous exposure amount determinedabove. Namely, it is expressed as:

percutaneous safety coefficient=percutaneous non-influential amount[mg/kg/day]/estimated percutaneous exposure amount [mg/kg/day]

Nevertheless, in general, percutaneous non-influential amount has notoften been determined, and there are not many published values.Accordingly, a more accurate value can be determined from the estimatedpercutaneous exposure amount, and oral non-influential amount andpercutaneous absorption ratio for which many published values exist,according to the following expression:

percutaneous safety coefficient=oral non-influential amount[mg/kg/day]/(estimated percutaneous exposure amount[mg/kg/day]×percutaneous absorption ratio [%])

Here, when the percutaneous absorption ratio is unknown, employed is anational guideline (e.g., 10%) which usually exists.

(vi) Calculation of Estimated Oral Exposure Amount and Oral SafetyCoefficient (S13 and S14)

From the estimated percutaneous exposure amount obtained in theabove-mentioned item (v), hand surface area ratio, and oral transferenceratio, the estimated oral exposure amount from hand to mouth isdetermined. Namely, calculation of:

estimated oral exposure amount [mg/kg/day]=estimated percutaneousexposure amount [mg/kg/day]×hand surface area ratio [%]×oraltransference ratio [%]

is effected. Here, the hand surface area ratio is expressed by (handsurface area/body surface area), for which a published value (e.g.,5[%]) may be used. The oral transference ratio is a hypothetical value,which is set to 100%, for example.

In the case where oral exposure might occur via tableware or foodcontaminated with the residually sprayed compound, it is required thatthe estimated oral exposure amount from tableware or food to mouth beadded to the estimated oral exposure amount from hand to mouth to yieldthe total estimated oral exposure amount. For example, the estimatedoral exposure amount from tableware is obtained when, according to thetableware residual amount indicating the amount of the harmful materialremaining in tableware, tableware use area which is the sum of tablewaresurface areas, and oral transference ratio from tableware, calculationof:

estimated oral exposure amount [mg/kg/day]=tableware residual amount[mg/m²]×tableware use area [m²/day]×oral transference ratio [%]/bodyweight [kg]

is effected. Here, the tableware residual amount is expressed by (meanfloor residual amount×tableware contamination ratio). As the tablewarecontamination ratio, an actually measured value (e.g., 9%) or ahypothetical value may be used.

The oral safety coefficient is computed from the non-influential amountconcerning oral toxicity examined by an animal experiment beforehand andthe estimated oral exposure amount determined above. Namely, it isexpressed as:

oral safety coefficient=oral non-influential amount[mg/kg/day]/estimated oral exposure amount [mg/kg/day]

As mentioned in the foregoing, in the method of estimating an indoorbehavior of a pesticidal compound in this embodiment, the environment isdivided into the condensed particles 9, 10, and 11 that are classifiedinto three kinds depending on occurrence and extinction, thehigh-concentration air 12, medium-concentration air 13, andlow-concentration air 14 that are classified into three kinds dependingon the compound concentration, the floor 5, the wall 6, and thehigh-concentration ceiling 15, medium-concentration ceiling 16, andlow-concentration ceiling 17 that are classified into three kindsdepending on the compound concentration; and differential equationsconcerning Fugacity in these members are simultaneously formed and aresolved, whereby the indoor behavior of the compound when heat-vaporizinga chemical containing the compound is estimated. Here, when solving thesimultaneous differential equations, the estimation nick time width isvariably set, while constantly confirming mass balance of the compoundindoors after the spraying, so that the amount of input of the chemicalindoors and the resulting solution coincide with each other.

Accordingly, since mass balance of the compound after the spraying isalways monitored such that the amount of input of the compound indoorsand the resulting solution coincide with each other, thereby varying theestimation nick time width; the estimation nick time width is set longerwhen the mass balance fluctuates a little, whereas it is set shorterwhen the mass balance starts fluctuating greatly. Namely, when solvingsimultaneous differential equations including a parameter accompanyingtemporal change, the estimation nick time width is automatically set inresponse to the fluctuation in mass balance. Consequently, whenprocessed by a computer, an accurate solution can be obtained in a shorttime.

The method of evaluating safety of a pesticidal compound in accordancewith this embodiment uses the estimated result mentioned above toevaluate the safety of the compound with respect to the human body whenthe chemical is heated to vaporize.

Accordingly, the safety of the compound with respect to the human bodycan be evaluated accurately in a short time. As a consequence, whenformulating a chemical such as insecticide containing the compound,simulation can be easily repeated while changing conditions, therebymaking it easier to formulate a chemical having a high safety conformingto the aimed object.

Though the kind of the floor 5 is assumed to be tatami in thisembodiment, differential equations similar to those mentioned above mayalso be formed in the case of flooring. In this case, however, whendetermining fugacity capacity (Z₅) of the floor 5 in equation (60), itis necessary for the particle-constituting solvent component content(see Table 27) to be changed from that of tatami to that of flooring.

Though Fugacity is determined by use of Runge-Kutta-Gill method in thisembodiment, other methods may be used for solving differentialequations. Runge-Kutta-Gill method, however, is preferably used since aprogram for the above-mentioned differential equations can be easilymade by Basic. Also in the case where differential equations are solvedby a method other than Runge-Kutta-Gill method, similar effects can beobtained when the estimation nick time width is set as mentioned above.

(6) Sixth Embodiment

With reference to the drawings, the sixth embodiment of the presentinvention will be explained in the following. The method of simulatingan indoor behavior of a pesticidal compound in accordance with thisembodiment estimates the behavior of the compound in the case where thefloor in the fifth embodiment is constituted by a rug having ears offiber. For convenience of explanation, members identical to those shownin the drawings of the previous embodiment will be referred to withnumerals or letters identical thereto, without their explanationsprovided. Explained here is a case where the kind of floor is a carpet.Accordingly, only the portion different from the fifth embodiment willbe explained.

First, the carpet is modeled as shown in FIGS. 13A, 13B, and 13C.Namely, the carpet is divided into a plurality of carpet fibers (ears offiber) planted on a substrate and space portions existing between thefibers. When a chemical is heated to vaporize in a room in which such acarpet covers the whole floor surface, as condensed particles fall onthe carpet, the chemical infiltrates into the carpet fiber andaccumulates in the space portion.

While the method of simulating an indoor behavior of a pesticidalcompound in accordance with this embodiment also conforms to theflowchart of FIG. 1, at S1, as the primary condition, the carpet-relatedprimary condition shown in Table 31 is added to the primary condition ofthe fifth embodiment (see Tables 25 to 28). Here, the cross-sectionalarea (A_(c)) of the space portion of the carpet refers to the area inwhich the space portion is in contact with the indoor air (see FIGS.13A, 13B, and 13C).

TABLE 31 CARPET - RELATED EXAMPLE OF PRIMARY CONDITION SYMBOL VALUECARPET CROSS - SECTIONAL AREA OF A_(c) 1.6 × 10⁻³ SPACE PORTION OFCARPET [m²/m² FLOOR] AREA IN WHICH CARPET A_(c5) 0.192 FIBER IS INCONTACT [m²/m² FLOOR] WITH COMPOUND IN SPACE PORTION AREA IN WHICHCARPET A_(a5) 1.19 FIBER IS IN CONTACT [m²/m² FLOOR] WITH COMPOUNDPRODUCT PROPERTY CONTENT OF SOLVENT C_(sd) (XYLENE) CONTAINED IN PRODUCTDILUTION OF PRODUCT X_(sol)

The examples of values in Table 31 are based on the values shown inFIGS. 13A, 13B, and 13C. Here, one space portion is set to a size of 0.1[mm]×0.1 [mm]×3 [mm], and one square of carpet fiber is set to a size of2.5 [mm]×2.5 [mm]×3 [mm]. Also, it is assumed that 16 [pieces] of carpetfiber exist in 1 [cm²].

In this case, the individual parameters can be determined as:

A_(c) = (0.1 [mm] × 0.1 [mm] × 16 [pieces])/1 [cm] = 1.6 × 10⁻³ [m²/m²floor] A_(c5) = (0.1 [mm] × 3 [mm] × 4 [faces] × 16 [pieces])/1 [cm] =0.192 [m²/m² floor] A₅ = 1 − A_(c) = 1 − 1.6 × 10⁻³ [m²/m² floor] A_(a5)= A₅ + A_(c5) = 1.19 [m²/m² floor]

Here, A₅ is the area in which the carpet fibers in 1 [m²] are in contactwith the indoor air.

As the secondary condition at S2, the carpet-related secondary conditionshown in Table 32 is added to the secondary condition of the fifthembodiment. Here, k₅ and V₅, which are respectively transference speedof the compound in the floor and the volume of the floor in the fifthembodiment (see Table 30), are respectively replaced by the transferencespeed of the compound in the carpet fiber and the volume of the wholefiber of the carpet.

TABLE 32 SYM- CARPET - RELATED SECONDARY CONDITION BOL DEFINITE FACTORCONDITION EVAPORATION CONSTANT OF CHEMICAL R_(d) IN SPACE PORTIONHUMIDITY AT TEMPERATURE (T_(d)) OF SPACE PORTION H_(m) VOLUME OF WHOLEFIBER OF CARPET V₅ TRANSFERENCE SPEED OF COMPOUND IN PRODUCT k_(c)PROPERTY CHANGE CONSTANT OF PRODUCT a TEMPORAL CHANGE CONDITIONTRANSFERENCE COEFFICIENT OF COMPOUND D_(c14) BETWEEN CHEMICAL IN SPACEPORTION AND AIR TRANSFERENCE COEFFICIENT OF COMPOUND D_(c5) BETWEENCHEMICAL IN SPACE PORTION AND CARPET FIBER VOLUME OF CHEMICAL IN SPACEPORTION V_(c) FUGACITY CAPACITY OF CHEMICAL IN Z_(c) SPACE PORTION

A method of computing the definite factor conditions and temporal changeconditions shown in the above-mentioned Table 32 will be explainedhereinafter as exemplified by the case using an aqueous aerosol, i.e.,case where the particle-constituting solvent is water.

From the cross-sectional area (A_(c)) of the space portion, roomtemperature (T), and humidity (H), the evaporation constant (R_(d)) ofthe chemical entered into the space portion of the carpet is expressedas:

R _(d) =A _(c) h(H _(m) −H)/C _(H)

C _(H)=0.24+0.46H

h=3.06×10⁻⁴(T−T _(d))^(1/3)  (78)

wherein T_(d) is the temperature of the space portion of the carpet(corresponding to the wet-bulb temperature), and H_(m) is the humidity(corresponding to the saturated humidity at the wet-bulb temperature) ofthe space portion at T_(d). Here, T_(d) and H_(m) can be determined fromthe above-mentioned “mass-based humidity table” according to the roomtemperature (T) and humidity (H). In the case of an oil-based product(aerosol), while the vapor constant of the chemical can be computed whenproperties of the water and oil are compared with each other and thenare multiplied by R_(d), R_(d)=0 may be assumed in the case where theevaporation of the oil is slow.

From the diffusion coefficient (D_(c)) and the area (A_(a5)) in whichthe carpet fiber is in contact with the compound, the volume (V₅) of thewhole fiber of the carpet is determined as:

V ₅=2{square root over (D_(c)t)} A _(a5)  (79)

The transference speed (k_(c)) of the compound in the product isexpressed as k₁₄/100 by use of k₄ (=Gv₄/A₁₄) which indicates thetransference speed of the compound in the indoor air.

From the above-mentioned transference speed (k_(c)) of the compound inthe product, transference speed (k₁₄) of the compound in the indoor air,floor area (L₄×W₄), cross-sectional area (A_(c)) of the space portion,Fugacity capacity (Z_(c)) of the chemical in the space portiondetermined by expression (82) which will be mentioned later, andFugacity capacity (Z₁₄) of the low-concentration air determined byexpression (59) of the fifth embodiment, the transference coefficient(D_(c14)) of the compound between the chemical in the space portion ofthe carpet and the low-concentration air is expressed as:$\begin{matrix}{D_{c14} = \frac{1}{{1/\left( {k_{c}A_{c}L_{4}W_{4}Z_{c}} \right)} + {1/\left( {k_{14}A_{c}L_{4}W_{4}Z_{14}} \right)}}} & (80)\end{matrix}$

From the above-mentioned transference speed (k_(c)) of the compound inthe product, diffusion coefficient (D_(c)), floor area (L₄×W₄), area(A_(c5)) in which the carpet fiber is in contact with the compound inthe space portion, Fugacity capacity (Z_(c)) of the chemical in thespace portion, and Fugacity capacity (Z₅) of the floor determined byexpression (60) of the fifth embodiment, the transference coefficient(D_(c5)) of the compound between the chemical in the space portion andthe carpet fiber is expressed as; $\begin{matrix}{D_{c5} = \frac{1}{{1/\left( {k_{c}A_{c5}L_{4}W_{4}Z_{c}} \right)} + {1/\left( {k_{5}A_{c5}L_{4}W_{4}Z_{5}} \right)}}} & (81)\end{matrix}$

wherein k₅ (=(D_(c)/t)^(0.5)) is the transference speed of the compoundwithin the carpet fiber.

The volume (V_(c)) of the chemical in the space portion is determinedfrom the floor area (L₄×W₄), emission rate (E_(T)), condensation rate(C_(r)), and evaporation constant (R_(d)) of the chemical in the spaceportion determined by expression (78). The volume (V_(c)) of the spaceportion decreases until the solvent in the chemical completelyevaporates.

From the vapor pressure (P^(s)), water solubility (C^(s)), andoctanol/water distribution coefficient (K_(ow)) of the compound, andproperty change constant (a) of the product, Fugacity capacity (Z_(c))of the chemical in the space portion is expressed as follows:

Z _(c)=(e ^(−at) K _(OW)+1−e ^(−at))C ^(s) /P ^(s)  (82)

Here, the property change constant (a) of the product can be computedaccording to the evaporation constant (R_(d)) of the chemical in thespace portion determined by expression (78), content (C_(sd)) of thesolvent (Xylene) contained in the product, and dilution (X_(sol)) of theproduct. Namely, Fugacity capacity (Z_(c)) of the chemical in the spaceportion is also expressed as:

 Z _(c)=[(ratio of organic solvent in product)K _(ow)+(ratio of water inproduct)]×C^(s) /P ^(s)

By simultaneously forming this expression and the above-mentionedexpression (82), the property change constant (a) of the product iscomputed. Here, in the case of the oil-based product (aerosol), Fugacitycapacity (Z_(o)) of the chemical in the space portion is given byexpression (57) of the fifth embodiment from the vapor pressure (P^(s)),water solubility (C^(s)), and octanol/water distribution coefficient(K_(ow)) of the compound.

Consequently, the behavior of the compound in the space portion of thecarpet is expressed in the form of differential equation concerningFugacity (f_(c)) as follows: $\begin{matrix}\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{c}}{t}V_{c}Z_{c}} = {{\gamma_{c}{\sum\limits_{i = 9}^{11}{n_{i}A_{a5}V_{i}Z_{i}f_{i}}}} +}} & {{{Deposition}(i)}} \\{{{R_{d}L_{4}W_{4}Z_{c}f_{c}} +}} & {{V\text{-}{change}}} \\{{{D_{cj}\left( {f_{c} - f_{j}} \right)} +}} & {{{Transference}(j)}} \\{{{D_{c13}\left( {f_{c} - f_{13}} \right)} -}} & {{{Transfernce}(k)}} \\{{K_{c}V_{c}Z_{c}f_{c}}} & {{Degradation}}\end{matrix} & (83)\end{matrix}$

Also, expressions (71) and (70) in the fifth embodiment are respectivelyreplaced by the following expressions (84) and (85): $\begin{matrix}\begin{matrix}{{\frac{f_{5}}{t}V_{5}Z_{5}} = {{\sqrt{D_{c}/t}\quad A_{5}Z_{5}f} +}} & {{V - {change}}} \\{{{\sum\limits_{i = 9}^{11}{n_{i}V_{i}Z_{i}f_{i}}} +}} & {{{Deposition}(i)}} \\{{{D_{c5}\left( {f_{5} - f_{c}} \right)} +}} & {{{Transference}(c)}} \\{{{D_{145}\left( {f_{5} - f_{14}} \right)} -}} & {{{Transfernce}(14)}} \\{{K_{5}V_{5}Z_{5}f_{5}}} & {{Degradation}}\end{matrix} & (84) \\\begin{matrix}{{\frac{f_{14}}{t}V_{14}Z_{14}} = {{G\quad V_{14}Z_{14}f_{14}} -}} & {{Ventilation}} \\{{{\sum\limits_{i = 9}^{11}{n_{i}{D_{i14}\left( {f_{14} - f_{i}} \right)}}} -}} & {{{Transference}(i)}} \\{{{\sum\limits_{{j = 5},13,14}{D_{14j}\left( {f_{14} - f_{j}} \right)}} -}} & {{{Transference}(j)}} \\{{{K_{14}V_{14}Z_{14}f_{14}} -}} & {{Degradation}} \\{{D_{14c}\left( {f_{14} - f_{c}} \right)}} & {{{Transference}(c)}}\end{matrix} & (85)\end{matrix}$

Namely, as shown in expression (84), the differential equationconcerning the floor (carpet fiber) includes, in addition to expression(71) of the fifth embodiment, the terms of Deposition (i) indicating theamount of deposition of condensed particles onto the carpet fiber andTransference (c) indicating the amount of transference of the compoundbetween the carpet fiber and the space portion

In expression (85), which is differential equation concerning thelow-concentration air, terms of ventilation, Transference (i),Transference (j), Degradation, and Transference (c) respectivelyindicate the amount of discharge of the compound outdoors, amount oftransference of the compound between the low-concentration air andcondensed particles, amount of transference of the compound between thelow-concentration air and the medium-concentration air and floor, amountof degradation of the compound by light and oxidation, and amount oftransference of the compound between the low-concentration air and thespace portion.

Accordingly, Fugacity calculation at S3 is performed such that 12 kindsof differential equations of expressions (67) to (69) and (72) to (75)in the fifth embodiment and the above-mentioned expressions (83) to (85)are solved by Runge-Kutta-Gill method. The subsequent steps of S4 to S17are similar to those in the fifth embodiment.

As explained in the foregoing, in the method of estimating an indoorbehavior of a pesticidal compound in accordance with this embodiment, inthe case where the kind of floor is a carpet having ears of fiber and aspace portion between the ears, a differential equation for Fugacity inthe above-mentioned space portion of the carpet is added to 11 kinds ofsimultaneous differential equations concerning Fugacity in 3 kinds ofcondensed particles, air divided into 3 kinds depending on the compoundconcentration, floor, wall, and ceiling divided into 3 kinds dependingon the compound concentration, so as to calculate Fugacity.

Consequently, even in the case where the chemical is accumulated in thespace portion, so that the compound behaves differently from the casewith a flat floor, the behavior of the compound can be estimatedaccurately, whereby various kinds of simulations can be performed.

(7) Seventh Embodiment

With reference to the drawings, the seventh embodiment of the presentinvention will be explained in the following.

The method of simulating an indoor behavior of a pesticidal compound(hereinafter simply referred to as compound) contained in a chemical(solution) such as insecticide in accordance with this embodimentestimates the behavior of the compound in the case where the chemical issprayed over the whole floor surface, and is applied to the case where acarpet (rug) made of polymer fiber is spread on the whole floor surface.Here, usable as the chemical are pyrethroid insecticidal compounds,organophosphorus compounds, carbamate compounds, insect growthrestrainers (IGR), and the like. Its solvent may be water or oil.Explained in this embodiment is the case where the solvent is water. Thevermin to be killed is mainly flea, mite, and the like.

First, the carpet is modeled as shown in FIGS. 13A, 13B, and 13C.Namely, the carpet is divided into a plurality of carpet fibers (ears offiber) planted on a substrate and space portions existing between thefibers. When a chemical is sprayed over the whole floor area coveredwith a carpet, since the solvent of the chemical is water, the chemicalinfiltrates into the carpet fiber and accumulates in the space portion.The chemical not only attaches to the floor but also is partly suspendedin the air.

Accordingly, as shown in FIG. 17, the indoor environment covered withthe carpet is classified into seven kinds of media comprising the spaceportion of the carpet, two kinds of suspended large and small particleshaving different diameters, whole indoor air, floor (carpet fiber),wall, and ceiling.

The suspended particles are divided into two kinds since the behavior ofthe particles mainly depend on their diameter. Namely, while theindividual particles are distributed in the same place immediately afterspraying, as time passes, the large particles are distributed to aparticle zone DZ₂ close to the floor due to their weight, and the smallparticles are distributed to a particle zone DZ₃ close to the ceilingsince they are lighter than the large particles.

Simultaneous differential equations concerning Fugacity of the compoundin the above-mentioned seven kinds of media are formed and are solved byRunge-Kutta-Gill method, whereby the indoor behavior of the compound inthe chemical when the chemical is sprayed over the whole carpet surface,i.e., temporal change in the compound distribution in the room andamount of attachment to the interior materials of the floor, wall,ceiling, and the like, is estimated and analyzed.

With reference to FIG. 1, a method of simulating an indoor behavior ofthe compound will be explained. The simulation method in accordance withthis embodiment can be mainly divided into a step of dividing an indoorenvironment into predetermined media and forming a differential equationconcerning a fugacity of the compound in each medium (S1 to S2); a stepof determining the fugacity of the compound in each medium from thedifferential equation (S3); a step of determining the indoor behavior ofthe compound from the fugacity of the compound in each medium (S4); astep of changing, in response to a fluctuation in mass balance of thecompound indoors, a minute time unit used when solving the differentialequation (S21 to S35, see FIG. 5); and a step of evaluating safety ofthe compound with respect to a human body according to the indoorbehavior of the compound (S5 to S17).

First, at step (hereinafter abridged as S) 1, a primary condition isinputted. The primary condition comprises physicochemical properties ofthe compound (see Table 33), indoor environmental behavior properties ofthe compound (see Table 34), indoor environment (see Table 35), a carpetcondition (see Table 36), and product properties (see Table 37).

TABLE 33 PHYSICOCHEMICAL SYM- EXAMPLE PROPERTY OF COMPOUND BOL OF VALUEMOLECULAR WEIGHT M 350.46 [mole] SPECIFIC GRAVITY ρ 1 [g/cm³] VAPORPRESSURE P^(S) 6.7 × 10⁻³ [Pa] WATER SOLUBILITY C^(S) 1.1 × 10⁻³[mole/m³] OCTANOL/WATER K_(OW) 10^(5.1) DISTRIBUTION COEFFICIENT

TABLE 34 INDOOR ENVIRONMENTAL BEHAVIOR PROPERTY EXAMPLE OF COMPOUNDSYMBOL OF VALUE HALF-LIFE OF DEGRADATION BY LIGHT/OXIDATION IN CARPETSPACE PORTION τ_(c) SUSPENDED PARTICLE τ_(i) (i = 2, 3) AIR τ₄ 1.89 ×10⁵ FLOOR/WALL/CEILING τ_(j) (j = 5, 6, 7) [sec] DIFFUSION COEFFICIENTIN D_(c) 4.52 × 10⁻¹⁵ [m²/s] FLOOR/WALL/CEILING

TABLE 35 SYM- EXAMPLE INDOOR ENVIRONMENT BOL OF VALUE ROOM SIZE V₄  23.3[m³] TEMPERATURE T 298 [K] RELATIVE HUMIDITY φ  60 [% RH] ABSOLUTEHUMIDITY H 1.9 × 10⁻² [kg-H₂O/kg/dry air] VENTILATION RATE G  0.58 [l/h]INDOOR VAPOR PRESSURE P^(∞) 1.89 × 10³ IN PARTICLE - [Pa] CONSTITUTINGSOLVENT AIR DIFFUSION D_(air) 8.64 × 10⁻² COEFFICIENT [m²/h] HERE, V₄ =L₄ × W₄ × H₄ (= 3.6 m × 2.7 m × 2.4 m).

TABLE 36 SYM- EXAMPLE CARPET CONDITION BOL OF VALUE CROSS - SECTIONALAREA OF A_(c) 1.6 × 10⁻³ SPACE PORTION OF CARPET [m²/m² FLOOR] AREA INWHICH CARPET FIBER IS A_(c5) 0.192 IN CONTACT WITH COMPOUND [m²/m²FLOOR] IN SPACE PORTION AREA IN WHICH CARPET FIBER IS A_(a5) 1.19 INCONTACT WITH COMPOUND [m²/m² FLOOR]

TABLE 37 SYM- EXAMPLE PRODUCT PROPERTY BOL OF VALUE COMPOUND CONTENTC_(a) 0.5 [%] SPRAY RATIO — 25.4 [ml/m²] RATIO OF CHEMICAL — 60 [%]ATTACHING TO FLOOR CONTENT OF SOLVENT C_(sd) — (XYLENE) CONTAINED INPRODUCT DILUTION OF PRODUCT X_(sol) — DIAMETER OF SUSPENDED PARTICLELARGE PARTICLE d₀₂ 10 [μm] SMALL PARTICLE d₀₃ 1 [μm] DISTRIBUTION OFSUSPENDED PARTICLE LARGE PARTICLE — ABOUT 40 [%] SMALL PARTICLE — ABOUT0.006 [%] SPACE WIDTH OF SUSPENDED PARTICLE LARGE PARTICLE H₍₂₎ 2 [m]SMALL PARTICLE H₍₃₎ 1 [m]

The examples of values in Table 35 assume those of a six-mat room (9.72[m²]) of a typical apartment in Japan.

The cross-sectional area (A_(c)) of the space portion of the carpet inTable 36 is an area in which the space portion is in contact with theindoor air (see FIGS. 13A, 13B, and 13C). Further, the examples ofvalues in Table 36 are based on the values shown in FIGS. 13A, 13B, and13C. Here, one space portion is set to a size of 0.1 [mm]×0.1 [mm]×3[mm], and one square of carpet fiber is set to a size of 2.5 [mm]×2.5[mm]×3 [mm]. Also, it is assumed that 16 [pieces] of carpet fiber existin 1 [cm²].

In this case, the individual parameters can be determined as;

A_(c) = (0.1 [mm] × 0.1 [mm] × 16 [pieces])/1 [cm] = 1.6 × 10⁻³ [m²/m²floor] A_(c5) = (0.1 [mm] × 3 [mm] × 4 [faces] × 16 [pieces])/1 [cm] =0.192 [m²/m² floor] A₅ = 1 − A_(c) = 1 − 1.6 × 10⁻³ [m²/m² floor] A_(a5)= A₅ + A_(c5) = 1.19 [m²/m² floor]

Here, A₅ is the area in which the carpet fibers in 1 [m²] are in contactwith the indoor air.

Subsequently, using the primary condition, a secondary condition isdetermined by calculation (S2). The secondary condition comprises atemporally unchangeable definite factor condition (see Table 38)determined by the primary condition alone, and a temporal changecondition accompanying a temporal change (see Table 39). Theircalculations will be explained later in detail.

TABLE 38 DEFINITE FACTOR CONDITION SYMBOL EVAPORATION CONSTANT OF αSUSPENDED PARTICLES VOLUME RATIO OF COMPOUND IN PRODUCT R_(a) DIFFUSIONCOEFFICIENT OF D_(ca) COMPOUND IN AIR EVAPORATION CONSTANT OF R_(d)CHEMICAL IN SPACE PORTION FUGACITY CAPACITY OF SUSPENDED PARTICLE Z_(i)(i = 2, 3) AIR Z₄ FLOOR/WALL/CEILING Z_(j) (j = 5, 6, 7) DEGRADATIONCONSTANT OF CARPET SPACE PORTION K_(c) SUSPENDED PARTICLE K_(i) (i = 2,3) AIR K₄ FLOOR/WALL/CEILING K_(j) (‘= 5, 6, 7)

TABLE 39 TEMPORAL CHANGE CONDITION SYMBOL SUSPENDED PARTICLE DIAMETERd_(i) (i = 2, 3) FALLING SPEED v_(i) (i = 2, 3) SUSPENDED NUMBER n_(i)(i = 2, 3) TRANSFERENCE SPEED OF COMPOUND BETWEEN CHEMICAL IN SPACED_(c4) PORTION AND AIR BETWEEN CHEMICAL IN SPACE D_(c5) PORTION ANDCARPET FIBER BETWEEN SUSPENDED PARTICLE AND AIR D_(i4) (i = 2, 3)BETWEEN FLOOR/WALL/CEILING AND AIR D_(4j) (j = 5, 6, 7) VOLUME OFCHEMICAL IN SPACE PORTION VOLUME OF SUSPENDED PARTICLE D_(i) (i = 2, 3)VOLUME OF FLOOR/WALL/CEILING D_(j) (j = 5, 6, 7) FUGACITY CAPACITY OFCHEMICAL Z_(c) IN SPACE PORTION

Using the secondary condition, seven kinds of Fugacity are calculated(S3). Namely, seven kinds of differential equations concerning the spaceportion of the carpet, two kinds of large and small suspended particles,indoor air, floor (carpet fiber), wall, and ceiling are simultaneouslyformed and are solved by Runge-Kutta-Gill method, whereby seven kinds ofFugacity are computed over time. Here, an estimation nick time width(minute time unit) set when solving the differential equations isautomatically set so as to be varied in response to a fluctuation inmass balance of the compound.

At S4, using thus computed Fugacity of the small particles (takingaccount of Fugacity of the large particles when necessary) and Fugacityof the indoor air, temporal concentration of the compound in the air iscomputed; whereas floor residual amount of the compound is computed byuse of Fugacity of the carpet fiber and carpet space portion.

At S5, it is judged whether or not to perform safety evaluation in thecase where the chemical is inhaled. If the safety evaluation ininhalation is to be performed, then an estimated exposure amount ininhalation indicating a degree of exposure upon inhalation of thecontaminated air is computed by use of the above-mentioned temporalconcentration in the indoor air (S6). Thereafter, an inhalation safetycoefficient is computed according to the estimated exposure amount ininhalation (S7). At S8, the inhalation safety coefficient is comparedwith a reference value defined in each country. If the inhalation safetycoefficient exceeds the reference value, it is judged that “there is noproblem in safety.” By contrast, if the inhalation safety coefficient islower than the reference value at S8, it is judged that “there is aproblem in safety,” and the operation returns to S1, where alteration ofthe primary condition such as alteration of compound, alteration ofchemical formulation, alternation of using condition, or the like isconsidered.

If the safety evaluation in inhalation is not selected at S5, calculatedis an estimated amount of percutaneous exposure indicating to whatextent the skin is exposed in contact with the floor to which thechemical is attached (S9). Thereafter, at S10, it is judged whether toperform a percutaneous safety evaluation or not. If the percutaneoussafety evaluation is to be performed, a percutaneous safety coefficientis computed according to the estimated percutaneous exposure amount(S11). At S12, as with the safety evaluation in inhalation, thepercutaneous safety coefficient is compared with a reference valuedefined in each country, whereby the safety is evaluated. If there is aproblem in safety at S12, the operation returns to S1, where alterationof the primary condition is considered.

If the percutaneous safety evaluation is not selected at S10, calculatedat S13 according to the estimated percutaneous exposure amount is anestimated oral exposure amount indicating the degree of exposure in thecase where the chemical attached to a hand or the like is taken orally(S13). Subsequently, according to the estimated oral exposure amount, anoral safety coefficient is computed (S14). This oral exposure may occur,in particular, when an infant puts a chemical-attached hand into themouth. At S15, as with the safety evaluation in inhalation, the oralsafety coefficient is compared with a reference value defined in eachcountry, whereby the safety is evaluated. If there is a problem insafety at S15, the operation returns to S1, where alteration of theprimary condition is considered.

Finally, if it is judged to be safe at S8, S12, or S15, overall safetyis evaluated. Here, the sum of respective reciprocals of the previouslydetermined inhalation safety coefficient, percutaneous safetycoefficient, and oral safety coefficient is determined, and thereciprocal of thus determined value is defined as an overall safetycoefficient (S16). This overall safety coefficient is compared with areference value, whereby an evaluation similar to the previous safetyevaluation is effected (S17).

In the following, the above-mentioned steps of S2 to S4, S6, S7, S9,S11, S13, and S14 will be explained in detail.

(i) Secondary Condition Calculation (S2)

Calculations of the definite factor condition shown in Table 38 and thetemporal change condition shown in Table 39 will be explained.

According to surface temperature (T_(d)) of particles, properties ofparticle-constituting solvent (vapor pressure P_(d), molecular weightM_(d), and specific gravity ρ_(d)), and indoor environment (airdiffusion coefficient D_(air), vapor pressure P^(∞), and roomtemperature T^(∞)), the evaporation constant (α) of the suspendedparticles is defined as follows: $\begin{matrix}{\alpha = {\frac{4\quad D_{air}M_{d}}{R\quad \rho_{d}}\left( {\frac{P_{d}}{T_{d}} - \frac{P\quad \infty}{T\quad \infty}} \right)}} & (86)\end{matrix}$

wherein R is a gas constant, and P_(d) (=2.26×10³ [Pa]), M_(d) (=18[g/mole]), and ρ_(d) (=1×10⁶ [μg/m³]) are assumed to be the values dueto properties of water. Also, in this case, T^(∞) (temperature at thesite far from particles) is set to room temperature (T), T_(d) to indoorwet-bulb temperature (=292.5 [K]), and P^(∞) (vapor pressure of water atthe site far from particles) to 1.89×10³ [Pa]. These values are thosewith room temperature (T) of 298 [K] and relative humidity of 60[% RH].

Here, T_(d) can be determined, according to the room temperature (T) andrelative humidity (H), from “mass-based humidity table” disclosed in“Kagaku Kikai no Riron to Keisan (Theory and Calculation of ChemicalMachines)” (Second Edition) (Saburo Kamei ed., Sangyo Tosho) or thelike. On the other hand, P_(d and P) ^(∞) can be computed from thefollowing expressions:

log₁₀ P _(d)=10.23−1750/(T _(d)−38)

log₁₀ P ^(∞)=8.23−1750/(T−38)+log₁₀ψ

wherein ψ is an indoor relative humidity.

From the cross-sectional area (A_(c)) of the space portion, roomtemperature (T), and humidity (H), the evaporation constant (R_(d)) ofthe chemical entered into the space portion of the carpet is expressedas:

R _(d) =A _(c) h(H _(m) −H)/C _(H)

C _(H)=0.24+0.46H

h=3.06×10⁻⁴(T−T _(d))^(1/3)  (87)

wherein H_(m) is a humidity at temperature (T_(d)). The chemical enteredinto the space portion of the carpet reduces its volume upon evaporationand finally disappears, leaving the compound. Thus left compoundinfiltrates through the carpet fiber.

From the surface temperature (T_(d)) of particles and the vapor pressure(P^(s)) of the compound, Fugacity capacity (Z_(i), i=2, 3) of the largeand small particles is expressed as: $\begin{matrix}\begin{matrix}{Z_{i} = \frac{6 \times 10^{6}}{P_{L}^{S}{RT}_{d}}} \\{P_{L}^{S} = {P^{S}\exp \left\{ {6.79\left( {{T_{M}/T_{d}} - 1} \right)} \right\}}}\end{matrix} & (88)\end{matrix}$

Though the vapor pressure of the compound in a liquid state (P_(L) ^(s))is computed by use of the melting point (T_(M)) of the compound andT_(d) here; in the case where T_(M) cannot be obtained, P_(L) ^(s) maybe set identical to the vapor pressure of the compound in a solid state(P^(s)).

From the room temperature (T), Fugacity capacity (Z₄) of the air isexpressed as follows: $\begin{matrix}{Z_{4} = \frac{1}{RT}} & (89)\end{matrix}$

Since the carpet fiber and wallpaper covering the floor/wall/ceiling areformed by polymers; from the vapor pressure (P^(s)), water solubility(C^(s)), and octanol/water distribution coefficient (K_(ow)) of thecompound, and from the oil component content (ρ_(j)) of the carpet fiberand wallpaper covering the floor/wall/ceiling, Fugacity capacity (Z_(j),j=5, 6, 7) of the floor/wall/ceiling is expressed as:

Z _(j)=ρ_(j) K _(OW) C ^(S) /P ^(S)  (90)

The degradation constants (K_(c)), (K_(i), i=2, 3), (K₄), (K_(j), j=5,6, 7) of the carpet space portion, suspended particles, air, andfloor/wall/ceiling are defined by use of their respective half-lives ofdegradation by light/oxidation (τ_(o)), (τ_(i)), (τ₄), and (τ_(j)) asfollows: $\begin{matrix}\left. \begin{matrix}{K_{c} = {0.693/\tau_{c}}} \\{K_{i} = {0.693/\tau_{i}}} \\{K_{4} = {0.693/\tau_{4}}} \\{K_{j} = {0.693/\tau_{j}}}\end{matrix} \right\} & (91)\end{matrix}$

Mainly generated in the seven kinds of media are degradation reactionscaused by light and oxidation, and the reaction speed quantity at thistime is represented by the product of degradation constant, volume, andFugacity capacity. Among the degradation constants shown in expression(91), the degradation constant (K₄) of the compound in the air is hardto actually measure, and it is not usually easy to determine this value.Accordingly, when the actually measured value is unavailable, it may bedetermined as computed by Atmospheric Oxidation program (Atkinson etal., 1984, Chem. Rev. Vol. 84, pp. 437-470) from the structural formulaof the compound. Also, from the viewpoint of securing safety ofinhabitants, the degradation constants in the particles and in theinterior materials (floor/wall/ceiling) may be nullified when theiractually measured values are unavailable.

Since the volume of particles decreases over time due to evaporation,using the evaporation constant (α) determined from expression (86) andthe diameter (d_(0i)) of suspended particle immediately after spraying(t=0), the diameter (d_(i), i=2, 3) of the suspended particles at time tis determined as:

d _(i) ={square root over (d_(0i) ²−2αt)}  (92)

d _(i) ={square root over (R_(a))} d _(0i)  (92′)

On the other hand, when the particle-constituting solvent in thesuspended particle is completely evaporated, the diameter (d_(i))becomes that of the compound alone, thereby being held constant. Namely,the particle diameter (d_(i)) after the complete evaporation of theparticle-constituting solvent is represented by the above-mentionedexpression (92′) by use of the volume ratio (R_(a)) of the compound inthe product and the diameter (d_(0i)) of the particles immediately afterspraying.

From the compound content (C_(a)) and the specific gravity (ρ) of thecompound, the volume ratio (R_(a)) of the compound in the product isexpressed as C_(a)/ρ.

As shown in FIG. 18, immediately after spraying the chemical, a particlezone (DZ_(i)) having a width (W₄), length (L₄), and space width(H_((i))) is formed at a certain height from the floor. In conformity tothe falling speed (v_(i)) of suspended particles, the particle zone(DZ_(i)) approaches the floor. When the bottom of the particle zone(DZ_(i)) reaches the floor, the compound in the suspended particlestransfers to the carpet space portion and carpet fiber.

Since movement of the particles is under the control of gravity and airresistance, according to Stokes' law using the diameter (d_(i)) ofsuspended particles determined by expression (92), the falling speed(v_(i), i=2, 3) of the suspended particles is represented by thefollowing expression (93): $\begin{matrix}{v_{i} = {{\frac{\rho \quad {gS}_{c}}{18\quad \eta}d_{i}^{2}} = {\beta \left( {d_{0i}^{2} - {2\quad \alpha \quad i}} \right)}}} & (93) \\{S_{c} = {1 + {\frac{2}{7.6 \times 10^{7}d_{i}}\left\lbrack {6.32 + {2.01\quad \exp \quad \left( {{- 8.322} \times 10^{6}d_{i}} \right)}} \right\rbrack}}} & \left( 93^{\prime} \right) \\{v_{i} = {\left( {\rho/\rho_{d}} \right)\beta \quad d_{i}^{2}}} & \left( 93^{''} \right)\end{matrix}$

wherein g is gravitational acceleration, η is the coefficient ofviscosity of the air, S_(c) is a sliding correction coefficient, and βis a speed coefficient. Here, while particles do not conform to theStokes' law when they become small, the sliding correction coefficient(S_(c)), which is a coefficient for correcting this phenomenon, isrepresented by the above expression (93′) according to the diameter(d_(i)) of particles determined by expression (92).

On the other hand, the falling speed (v_(i)) of the particles after thecomplete evaporation of particle-constituting solvent component isrepresented by the above expression (93″) using the specific gravity (ρ)of the compound, specific gravity (ρ_(d)) of the particle-constitutingsolvent, speed coefficient (β), and diameter (d_(i)) of particlesdetermined by expression (92′).

The number of suspended particles (n_(i), i=2, 3) also decreases uponexchange of the air through a window and the like. Here, the smallparticles float in conformity to the indoor air flow, and the largeparticles, which reduce their diameter as their volume decreases, areassumed to conform to the flow of the indoor air flow. In this case,during the period till the particle zone (DZ_(i)) reaches the floor, thenumber of particles (n_(i)) would decrease only upon ventilation of theroom. Accordingly, from the room size (V₄=L₄×W₄×H₄), ventilation rate(G), particle space width (H_((i))), i=2, 3), and particle falling speed(v_(i)) determined by expression (93) or (93″), the particle number(n_(i)) is expressed as follows: $\begin{matrix}{\frac{n_{i}}{t} = {{{- \frac{n_{i}}{H_{(i)}}}{Vi}} - {\frac{n_{i}}{L_{4}}k_{4}}}} & (94)\end{matrix}$

wherein k₄ (=GV₄/A₄) is the transference speed of the compound in theair.

From the floor size (L₄×W₄), ventilation rate (G), cross-sectional area(A_(o)) of the space portion, Fugacity capacity (Z_(o)) of the chemicalin the space portion determined by expression (101) mentioned later, andFugacity capacity (Z₄) of the air determined by expression (89), thetransference coefficient (D_(c4)) of the compound between the chemicalin the space portion and the air is represented as follows:$\begin{matrix}{D_{c4} = \frac{1}{{1/\left( {k_{c}A_{c}L_{4}W_{4}Z_{c}} \right)} + {1/\left( {k_{4}A_{c}L_{4}W_{4}Z_{4}} \right)}}} & (95)\end{matrix}$

wherein k_(c) (=k₄/100) is the transference speed of the compound on thewater surface of the chemical in the space portion.

From the diffusion coefficient (D_(p)), floor size (L₄×W₄), ventilationrate (G), Fugacity capacity (Z_(c)) of the chemical in the spaceportion, and Fugacity capacity (Z₅) of the floor determined byexpression (90), the transference coefficient (D_(c5)) of the compoundbetween the chemical in the space portion and the carpet fiber isrepresented as: $\begin{matrix}{D_{c5} = \frac{1}{{1/\left( {k_{c}A_{c5}L_{4}W_{4}Z_{c}} \right)} + {1/\left( {k_{5}A_{c5}L_{4}W_{4}Z_{5}} \right)}}} & (96)\end{matrix}$

wherein k₅ (=(D_(p)/t)^(0.5)) is the transference speed of the compoundin the carpet fiber, and A_(c5) is the contact area ratio of the carpetfiber and space portion relative to the floor.

The diffusion coefficient (D_(p)) of the compound in thefloor/wall/ceiling can be determined when the diffusion coefficient(D_(ca)) of the compound in the air is multiplied by 10⁻⁹, whereasD_(ca) can be computed from properties of the compound (e.g., structuralformula, molecular weight, and the like) according to Wike and Leemethod (“Handbook of Chemical Property Estimation Methods,” McGraw-HillBook Company, 1982), for example.

From the diameter (d_(i)) of particles determined by expression (92) or(92′), transference speed (k₄) of the compound in the air, falling speed(v_(i)) determined by expression (93) or (93″), Fugacity capacity(Z_(i)) and (Z₄) determined by expressions (88) and (89), thetransference coefficient (D_(i4)) of the compound between the suspendedparticles and the air becomes: $\begin{matrix}{D_{i4} = \frac{1}{\left. {{1/\left( {k_{i}A_{i}Z_{i}} \right)} + {1/\left\{ {\left( {k_{4} + v_{i}} \right)A_{i}Z_{4}} \right)}} \right\}}} & (97)\end{matrix}$

wherein Ai (=πd_(i) ²) is the surface area of suspended particles, andk_(i) (=k₄/100) is the transference speed of the compound in theparticle surface.

From the diffusion coefficient (D_(p)) of the floor/wall/ceiling, roomsize (L₄×W₄×Z₄), ventilation rate (G), and Fugacity capacity (Z₄) and(Z_(j)) determined by expressions (89) and (90), the transferencecoefficient (D_(4j)) of the compound between the air and thefloor/wall/ceiling becomes: $\begin{matrix}{D_{4j} = \frac{1}{{1/\left( {k_{4}A_{j}Z_{4}} \right)} + {1/\left( {k_{j}A_{j}Z_{j}} \right)}}} & (98)\end{matrix}$

wherein A_(j) is the surface area of the wall and ceiling, and k_(j)(=(D_(p)/t)^(0.5)) is the transference speed of the compound in thefloor/wall/ceiling.

The volume (V_(c)) of the chemical in the space portion is determinedfrom the floor size (L₄×W₄), spray rate, content (C_(sd)) of the solvent(xylene) contained in the product, dilution (X_(sol)) of the product,and evaporation constant (R_(d)) of the chemical in the space portiondetermined by expression (87). The volume (V_(c)) of the space portiondecreases until the particle-constituting solvent in the chemicalcompletely evaporates.

Since the suspended particles are mostly made of moisture(particle-constituting solvent), their volume decreases as time passes.Since the suspended particles reduce their volume till theparticle-constituting solvent completely evaporates, using diameter(d_(i)) of suspended particles determined by expression (92) or (92′)and the above-mentioned evaporation constant (α), the volume change(dV_(i)/dt) of suspended particles is expressed as follows:$\begin{matrix}{\frac{V_{i}}{t} = {{- \quad \frac{\pi}{2}}\alpha \quad d_{i}}} & (99)\end{matrix}$

Assuming that the floor/wall/ceiling before spraying the chemical islike a thin film and that, as the chemical infiltrates into the film,its thickness increases so as to enhance the volume thereof; from thediffusion coefficient (D_(p)) of the compound in the floor/wall/ceiling,the volume (V_(j)) of floor/wall/ceiling is represented as follows:

V _(j)=2(D _(p) t)^(0.5) A _(j)  (100)

Fugacity capacity (Z_(c)) of the chemical in the space portion isinitially expressed by K_(ow)C^(s)/P^(s) as with the above-mentionedFugacity of the floor/wall/ceiling. When the chemical beginsevaporating, Fugacity capacity (Z_(c)) gradually approaches C^(s)/P^(s)(Fugacity capacity of water). Accordingly, from the vapor pressure(P^(s)), water solubility (C^(s)), and octanol/water distributioncoefficient (K_(ow)) of the compound, and property change constant (a)of the product, Fugacity capacity (Z_(c)) is expressed as follows:

Z _(c)=(e ^(−at) K _(OW)+1−e ^(−at))C^(S)/P^(S)  (101)

Here, the property change constant (a) of the product can be computedaccording to the evaporation constant (R_(d)) of the chemical in thespace portion determined by expression (87), content (C_(sd)) of thesolvent (Xylene) contained in the product, and dilution (X_(sol)) of theproduct. Namely, Fugacity capacity (Z_(c)) of the chemical in the spaceportion is also expressed as:

Z _(c)=((ratio of organic solvent in diluted liquid)K _(ow)+(ratio ofwater in diluted liquid)]×C ^(s) /P ^(s)

By simultaneously forming this expression and the above-mentionedexpression (101), the property change constant (a) of the product iscomputed.

(ii) Fugacity Calculation (S3)

The behavior of the compound in the carpet space portion is expressed inthe form of differential equation concerning Fugacity (f_(c)) as:$\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{c}}{t}V_{c}Z_{c}} = \begin{matrix}{{\gamma_{s}{\sum\limits_{i = 2}^{3}{n_{i}v_{i}A_{c}V_{i}Z_{i}{f_{i}/H_{(i)}}}}} +} & {{Depostion}(i)} \\{{R_{d}L_{4}W_{4}Z_{c}f_{c}} -} & {V\text{-}{change}} \\{{\sum\limits_{k = 4}^{5}{D_{ek}\left( {f_{c} - f_{k}} \right)}} -} & {{Transference}\left( {4,5} \right)} \\{K_{c}V_{c}Z_{c}f_{c}} & {Degradation}\end{matrix}} & (102)\end{matrix}$

Here, the terms of Deposition (i), V-change, Transference (4,5), andDegradation respectively indicate the attachment accompanying thefalling of the suspended particles to the space portion, volume change(decrease over time) of the chemical in the space portion, amount oftransference of the compound between the space portion and the air andfloor (carpet fiber), and amount of degradation of the compound in thespace portion. Here, Fugacity (f_(c)) is effective till the chemical inthe space portion completely evaporates. Also, γ₅ indicates the ratio ofsuspended particles attaching to the floor.

The behavior of the compound in the large and small particles isexpressed in the form of differential equation concerning Fugacity(f_(i), i=2, 3) as: $\begin{matrix}\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{i}}{t}V_{i}Z_{i}} = {\frac{\pi}{2}\alpha \quad d_{i}Z_{i}f_{i}}} & {{V\text{-}{change}}} \\{{- {D_{i4}\left( {f_{i} - f_{4}} \right)}}} & {{{Transference}(4)}} \\{{{- K_{i}}V_{i}Z_{i}f_{i}}} & {{Degradation}}\end{matrix} & (103)\end{matrix}$

Here, the terms of V-change, Transference (4), and Degradationrespectively indicate the volume change (decrease over time) of thesuspended particles, amount of transference of the compound between theparticles and the air, and amount of degradation of the compound in theparticles. Here, with the lapse of time, particles are absorbed by thecarpet space portion and floor (carpet fiber), whereby Fugacity (f_(i))is lost.

The behavior of the compound in the indoor air is expressed in the formof differential equation concerning Fugacity (f₄) as: $\begin{matrix}\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{4}}{t}V_{4}Z_{4}} = {{- {GV}_{4}}Z_{4}f_{4}}} & {{Ventilation}} \\{{- {D_{c4}\left( {f_{4} - f_{c}} \right)}}} & {{{Transference}(c)}} \\{{- {\sum\limits_{i = 2}^{3}{n_{i}{D_{i4}\left( {f_{4} - f_{i}} \right)}}}}} & {{{Transference}(i)}} \\{{- {\sum\limits_{j = 5}^{7}{D_{4j}\left( {f_{4} - f_{j}} \right)}}}} & {{{Transference}(j)}} \\{{{- K_{4}}V_{4}Z_{4}f_{4}}} & {{Degradation}}\end{matrix} & (104)\end{matrix}$

Here, the terms of Ventilation, Transference (C), Transference (i),Transference (j), and Degradation respectively indicate the amount ofdischarge of the compound outdoors, amount of transference of thecompound between the air and the space portion, amount of transferenceof the compound between the air and the suspended particles, amount oftransference of the compound between the air and the floor/wall/ceiling,and amount of degradation of the compound in the air.

The behavior of the compound in the floor (carpet fiber) is expressed inthe form of differential equation concerning Fugacity (f₅) as:$\begin{matrix}\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{5}}{t}V_{5}Z_{5}} = {{\gamma_{s}{\sum\limits_{i = 2}^{3}{n_{i}v_{i}A_{a5}V_{i}Z_{i}{f_{i}/H_{(i)}}}}} -}} & {{Deposition}(i)} \\{{\sqrt{{D_{p}/t}\quad}A_{a5}Z_{5}f_{5}} -} & {V\text{-}{change}} \\{{D_{c5}\left( {f_{5} - f_{c}} \right)} -} & {{Transference}(c)} \\{{D_{45}\left( {f_{5} - f_{4}} \right)} -} & {{Transference}(4)} \\{K_{5}V_{5}Z_{5}f_{5}} & {Degradation}\end{matrix} & (105)\end{matrix}$

Here, the terms of Deposition (i), V-change, Transference (c),Transference (4), and Degradation respectively indicate the attachmentof the suspended particles accompanying falling to the carpet fiber,volume change (increase over time) of the floor, amount of transferenceof the compound between the carpet fiber and the space portion, amountof transference of the compound between the carpet fiber and the air,and amount of degradation of the compound in the carpet fiber.

The behavior of the compound in the wall and ceiling is expressed in theform of differential equation concerning Fugacity (f_(j), j=6, 7) as:$\begin{matrix}\begin{matrix}{\underset{F\text{-}{change}}{\frac{f_{j}}{t}V_{j}Z_{j}} = {{{- \sqrt{{D_{p}/t}\quad}}A_{j}Z_{j}f_{j}} +}} & {V\text{-}{change}} \\{{r_{j}{\sum\limits_{i = 2}^{3}{n_{i}v_{i}V_{i}Z_{i}{f_{i}/H_{(i)}}}}} -} & {Deposition} \\{{D_{4j}\left( {f_{j} - f_{4}} \right)} -} & {Transference} \\{K_{j}V_{j}Z_{j}f_{j}} & {Degradation}\end{matrix} & (106)\end{matrix}$

Here, the terms of V-change, Transference (4), and Degradationrespectively indicate the volume change (increase over time) of thewall/ceiling, amount of transference of the compound between thewall/ceiling and the air, and amount of degradation of the compound inthe wall/ceiling. Also, γ_(j) is the ratio of suspended particlesattaching to the wall and ceiling.

The above-mentioned seven kinds of differential equations (102) to (106)are simultaneously formed and are solved by Runge-Kutta-Gill method, soas to compute Fugacity (f₂ to f₇, and f_(c))

When solving these simultaneous differential equations, it is necessaryto set an estimation nick time width (dt) which is a minute time unit.Namely, the estimation nick time width is used such that solutions ofthe simultaneous differential equations are initially determined at atime (t₀), and then solutions of the simultaneous differential equationsare determined at a time (t₀+dt) to which the estimation nick time widthis added. As solutions are obtained while estimation nick time widthsare successively added, temporally changing Fugacity can be determined.Theoretically, as the set time of the estimation nick time width isshorter, more accurate solutions can be obtained, though necessitating avery long calculation time. By contrast, when the set time is too long,solutions tend to diverge, thereby generating errors.

Therefore, in the present invention, the estimation nick time width isset shorter when a very large change occurs in a chemical, whereas it isset longer when there is no large change.

Specifically, mass balance is always confirmed such that the amount ofinput of the chemical and the resulting solution coincide with eachother, and the estimation nick time width is set longer when the massbalance does not fluctuate greatly, whereas it is set shorter when themass balance starts fluctuating. For example, when the fluctuation ofmass balance is set to an accuracy of ±5%, the estimation nick timewidth is always set so as to constantly satisfy the relationship of:

 compound input amount/(existing amount+degrading amount+dischargingamount)=0.95 to 1.05

namely, such that the fluctuation of mass balance lies within the rangeof ±5%.

Here, the above-mentioned compound input amount is determined by thefloor size (L₄×W₄), compound content (C_(a)), and spray rate. Since thetemporal amounts of compound in the seven kinds of media are determinedby the simultaneous differential equations, they are summed up so as tocompute the existing amount as shown in the following. Also, thedegrading amount and discharging amount are as follows: $\begin{matrix}{{{{existing}\quad {amount}} = {{V_{c}Z_{c}f_{c}} + {\sum\limits_{i = 2}^{3}{n_{i}f_{i}V_{i}Z_{i}}} + {\sum\limits_{k = 4}^{7}{f_{k}V_{k}Z_{k}}}}}{{{degrading}\quad {amount}} = {{K_{c}V_{c}Z_{c}f_{c}} + {\sum\limits_{i = 2}^{3}{K_{i}n_{i}f_{i}V_{i}Z_{i}}} + {\sum\limits_{k = 4}^{7}{K_{k}f_{k}V_{k}Z_{k}}}}}{{{discharging}\quad {amount}} = {{G\quad V_{4}Z_{4}f_{4}} + {\sum\limits_{i = 2}^{3}{G\quad n_{i}V_{i}Z_{i}f_{i}}}}}} & (107)\end{matrix}$

With reference to the flowchart of FIG. 5, the method of setting theestimation nick time width (dt) will be explained.

First, an initial value of estimation nick time width (dt) is inputted(S21). Then, an upper limit set value (e.g., 0.1[%]) which is the upperlimit of difference in mass balance, and a lower limit set value (e.g.,10⁻⁶[%]) which is the lower limit of difference in mass balance areinputted (S22). Thereafter, Fugacity and mass balance at t=t₀ arecalculated (S23 and S24), and Fugacity and mass balance at t=t+dt (ort₀+dt) are calculated (S25 and S26).

It is judged whether the fluctuation in mass balance is within the rangeof ±5% or not (S27). If the fluctuation in mass balance is within therange of ±5%, it is judged whether the difference between the massbalance at t=t (or t₀) and the mass balance at t=t+dt (or t₀+dt) is atleast the upper limit set value or not (S28). If it is judged to be atleast the upper limit set value at S28, then solutions become moreaccurate when the estimation nick time width (dt) is made shorter. Inthis case, the estimation nick time width (dt) is multiplied by ½ so asto change its setting (S29). When the difference is judged to be smallerthan the upper limit set value at S28, it is judged at S30 whether thedifference between the mass balance at t=t (or t₀) and the mass balanceat t=t+dt (or t₀+dt) is at most the lower limit set value or not.

When the mass balance difference is not greater than the lower limit setvalue at S30, since solutions are not influenced by longer estimationnick time width (dt), the estimation nick time width (dt) is doubled soas to change its setting (S31). Subsequently, it is judged whether theestimation nick time width (dt) changed at S31 is at most a maximumvalue (e.g., 0.1 [hour]) of estimation nick time width (dt) or not(S32). When the estimation nick time width (dt) is not greater than themaximum value at S32, since solutions do not diverge, the estimationnick time width (dt) set at S31 is used. When the estimation nick timewidth (dt) is greater than the maximum value at S32, since solutions maydiverge, the estimation nick time width (dt) is reset to the maximumvalue (S33). When the mass balance difference is greater than the lowerlimit set value at the above-mentioned S30, namely, when it lies betweenthe lower limit set value and upper limit set value, the calculationsare continued without changing the estimation nick time width (dt).

After the step of S29, S30, S32, or S33, the operation returns to S25 soas to effect calculation again, and this process is repeated till theaimed time is attained.

When the fluctuation in mass balance exceeds the range of ±5% at S27, onthe other hand, the mass balance fluctuation is so much that calculationis preferably effected with an estimation nick time width (dt) shorterthan that in the case where the fluctuation is within the range of ±5%.Accordingly, the calculation is stopped once (S34), the lower limit setvalue is reset to a lower level (S35), and then the operation returns tothe step of S23.

Thus, when the estimation nick time width is variably set without beingheld constant, while monitoring the mass balance fluctuation, Fugacitycan be computed accurately and efficiently.

(iii) Computation of Temporal Concentration in Indoor Air and FloorResidual Amount (S4)

The temporal concentration of the compound in the indoor air is computedwhen Fugacity (f₃) of the small particles, determined by theabove-mentioned item (ii), multiplied by Fugacity capacity (Z₃), andFugacity (f₄) of the indoor air multiplied by Fugacity capacity (Z₄) aresummed up. Here, in the case where the large particles may be inhaled bya human body depending on the kind of chemical, calculation is effectedwhile taking account of Fugacity (f₂) of the large particles as well.

The floor residual amount of the compound is computed when Fugacity (f₅)of the floor is multiplied by Fugacity capacity (Z₅). In the case wherethe solvent is water, in particular, it is preferably computed bysumming up the above-mentioned computed value (f₅, Z₅) and the valueobtained when Fugacity (f_(c)) of the space portion is multiplied byFugacity capacity (Z_(c)).

(iv) Calculation of Estimated Exposure Amount in Inhalation andInhalation Safety Coefficient (S6 and S7)

The above-mentioned temporal concentration in the indoor air forms acurve shown in FIG. 3A, for example. This concentration curve isintegrated, an accumulated concentration of the compound during aspecific period (t₁ to t₂) is determined (see FIG. 3B), and the meanconcentration in the indoor air is computed from thus determined value.While an arbitrary period is set as the specific period depending on theobject, an appropriate period is usually set in view of the method ofuse of the product and the test period of toxicity data.

Then, according to the above-mentioned mean concentration in the indoorair, amount of respiration, and exposure time, the estimated exposureamount in inhalation is determined. Namely, calculation of:

estimated exposure amount in inhalation [mg/kg/day]=mean concentrationin indoor air [mg/m³]×amount of respiration [m³/kg/min]×exposure time[min/day]

is effected. Here, as the above-mentioned amount of respiration, apublished value or actually measured value may be used. Also, whenamounts of respiration are respectively set for adult and child, moreappropriate estimated exposure amounts in inhalation can be obtained. Inthe case where the inhaled harmful material is not totally absorbed intothe body but is partially discharged by respiration, a more appropriateestimated exposure amount in inhalation can be obtained when theinhalation ratio is taken into account.

The inhalation safety coefficient is computed from a non-influentialamount concerning inhalation toxicity examined by an animal experimentbeforehand and the estimated exposure amount in inhalation determinedabove. Namely, it is expressed as:

inhalation safety coefficient=inhalation non-influential amount[mg/kg/day]/estimated exposure amount in inhalation [mg/kg/day]

(v) Calculation of Estimated Percutaneous Exposure Amount andPercutaneous Safety Coefficient (S9 and S11)

The above-mentioned floor residual amount forms a curve such as thatshown in FIG. 4A, for example. This residual amount curve is integrated,the accumulated residual amount of the compound during a specific period(t₁ to t₂) is determined (see FIG. 4B), and the mean residual amount iscomputed from thus determined value. While an arbitrary period is set asthe specific period depending on the object, an appropriate period isusually set in view of the method of use of the product and the testperiod of toxicity data.

Then, according to the mean floor residual amount, skin attachmentratio, contact area, and body weight, the estimated percutaneousexposure amount is determined. Namely, calculation of:

estimated percutaneous exposure amount [mg/kg/day]=(mean floor residualamount [mg/m²)×skin attachment ratio [%]×contact area [m²/day])/bodyweight [kg]

is effected. Here, as the contact area, a published value (e.g., 4[m²/day]) may be used. The skin attachment ratio is a ratio of thecompound attaching to the skin when the latter is in contact with thefloor where the compound exists. As this value, a published value or avalue experimentally obtained from a model may be used.

A model experiment method for the skin attachment ratio is as follows. Aweight (8 cm×8 cm×8 cm; 4.2 kg) is placed on a denim cloth (8 cm×10 cm)with a pressure similar to that of an infant in contact with a floor,and the denim cloth is pulled on the floor at a speed (120 cm/15 sec)similar to the moving speed of the infant. The denim and floor areanalyzed so as to compute the compound contained in the denim and floor.From the ratio therebetween, the skin attachment ratio is obtained. Ithas been confirmed that the skin attachment ratio obtained by thismethod is identical to or slightly higher than that determined fromanalyzed values of a hand and a floor when the hand is actually pressedagainst the floor, thereby proving this model experiment method to beuseful for evaluating exposure of inhabitants.

The percutaneous safety coefficient is computed from the non-influentialamount concerning percutaneous toxicity examined by an animal experimentbeforehand and the estimated percutaneous exposure amount determinedabove. Namely, it is expressed as:

percutaneous safety coefficient=percutaneous non-influential amount[mg/kg/day]/estimated percutaneous exposure amount [mg/kg/day]

Nevertheless, in general, percutaneous non-influential amount has notoften been determined, and there are not many published values.Accordingly, a more accurate value can be determined from the estimatedpercutaneous exposure amount, and oral non-influential amount andpercutaneous absorption ratio for which many published values exist,according to the following expression:

percutaneous safety coefficient=oral non-influential amount[mg/kg/day](estimated percutaneous exposure amount(mg/kg/day]×percutaneous absorption ratio [%])

Here, when the percutaneous absorption ratio is unknown, employed is anational guideline (e.g., 10%) which usually exists.

(vi) Calculation of Estimated Oral Exposure Amount and Oral SafetyCoefficient (S13 and S14)

From the estimated percutaneous exposure amount obtained in theabove-mentioned item (v), hand surface area ratio, and oral transferenceratio, the estimated oral exposure amount from hand to mouth isdetermined. Namely, calculation of:

estimated oral exposure amount [mg/kg/day]=estimated percutaneousexposure amount [mg/kg/day]×hand surface area ratio [%]×oraltransference ratio [%]

is effected. Here, the hand surface area ratio is expressed by (handsurface area/body surface area), for which a published value (e.g.,5[%]) may be used. The oral transference ratio is a hypothetical value,which is set to 100%, for example.

In the case where oral exposure might occur via tableware or foodcontaminated with the residually sprayed compound, it is required thatthe estimated oral exposure amount from tableware or food to mouth beadded to the estimated oral exposure amount from hand to mouth to yieldthe total estimated oral exposure amount. For example, the estimatedoral exposure amount from tableware is obtained when, according to thetableware residual amount indicating the amount of the harmful materialremaining in tableware, tableware use area which is the sum of tablewaresurface areas, and oral transference ratio from tableware, calculationof:

estimated oral exposure amount [mg/kg/day]=tableware residual amount[mg/m²]×tableware use area [m²/day]×oral transference ratio [%]/bodyweight [kg]

is effected. Here, the tableware residual amount is expressed by (meanfloor residual amount×tableware contamination ratio). As the tablewarecontamination ratio, an actually measured value (e.g., 9%) or ahypothetical value may be used.

The oral safety coefficient is computed from the non-influential amountconcerning oral toxicity examined by an animal experiment beforehand andthe estimated oral exposure amount determined above. Namely, it isexpressed as:

oral safety coefficient=oral non-influential amount[mg/kg/day]/estimated oral exposure amount [mg/kg/day]

As mentioned in the foregoing, in the method of estimating an indoorbehavior of a pesticidal compound in this embodiment, when a chemicalcontaining the above-mentioned compound is sprayed over the whole floorarea, differential equations concerning Fugacity of the space portionbetween carpet fibers, two kinds of large and small particles, indoorair, whole carpet fiber, wall, and ceiling are simultaneously formed andare solved, and the indoor behavior of the compound is estimatedaccording to thus obtained solution. Here, the estimation nick timewidth is variably set, while constantly confirming mass balance of thecompound indoors after the spraying, so that the amount of input of thechemical indoors and the resulting solution coincide with each other.

Accordingly, since mass balance of the compound after the spraying isalways monitored such that the amount of input of the compound indoorsand the resulting solution coincide with each other, thereby varying theestimation nick time width; the estimation nick time width is set longerwhen the mass balance fluctuates a little, whereas it is set shorterwhen the mass balance starts fluctuating greatly. Namely, when solvingsimultaneous differential equations including a parameter accompanyingtemporal change, the estimation nick time width is automatically set inresponse to the fluctuation in mass balance. Consequently, whenprocessed by a computer, an accurate solution can be obtained in a shorttime.

The method of evaluating safety of a pesticidal compound in accordancewith this embodiment uses the estimated result mentioned above toevaluate the safety of the compound with respect to the human body whenthe chemical is sprayed over the whole floor surface.

Accordingly, the safety of the compound with respect to the human bodycan be evaluated accurately in a short time. As a consequence, whenformulating a chemical such as insecticide containing the compound,simulation can be easily repeated while changing conditions, therebymaking it easier to formulate a chemical having a high safety conformingto the aimed object.

Though Fugacity is determined by use of Runge-Kutta-Gill method in thisembodiment, other methods may be used for solving differentialequations. Runge-Kutta-Gill method, however, is preferably used since aprogram for the above-mentioned differential equations can be easilymade by Basic. Also in the case where differential equations are solvedby a method other than Runge-Kutta-Gill method, similar effects can beobtained when the estimation nick time width is set as mentioned above.

Finally, a computer program product (storage medium) employed in each ofthe above-mentioned embodiments will be explained. FIG. 19 is aconfigurational view showing a storage medium 20 employed in each of theabove-mentioned embodiments of the present invention. As shown in FIG.19, the storage medium 20 comprises a program area 20 a for storing aprogram. This program area 20 a stores a pesticidal compound indoorbehavior simulation program 22. The pesticidal compound indoor behaviorsimulation program 22 comprises a main program 22 a for supervising theprocessing; a differential equation forming program 22 b for (S1)inputting a primary condition necessary for forming a differentialequation concerning a fugacity of the compound in each medium inresponse to an indoor environment divided into predetermined media and(S2) calculating a secondary condition so as to form the above-mentioneddifferential equation; a Fugacity calculating program 22 c for (S3)determining the fugacity of the compound from the above-mentioneddifferential equation; an indoor behavior calculating program 22 d for(S4) computing temporal concentration in indoor air and residual amount,which constitute an indoor behavior of the compound, from thuscalculated fugacity; a safety evaluating program 22 e for (S5 to S17)evaluating the safety of the compound with respect to a human bodyaccording to the temporal concentration in the indoor air and residualamount; and a minute time unit changing program 22 f for (S21 to S35)changing, in response to a fluctuation in mass balance of the compound,the minute time unit used when solving the differential equation. Theabove-mentioned letters and numerals within parentheses refer to thecorresponding steps in FIGS. 1 or 5.

As the storage medium 20, a disk-shaped storage medium such as flexibledisk or CD-ROM is used, for example. Alternatively, a tape-like storagemedium such as magnetic tape may be used as well.

The storage medium 20 may be used in an information processing apparatusshown in FIGS. 20 and 21. Namely, the information processing apparatus30 comprises a medium drive unit 32, which can accommodate the storagemedium 20. As the storage medium 20 is thus accommodated, theinformation stored therein can be accessed by the medium drive unit 32.Consequently, the pesticidal compound indoor behavior simulation program22 stored in the program area 20 a can be executed by the informationprocessing apparatus 30.

This information processing apparatus is configured as follows. First,it comprises the above-mentioned medium drive unit 32, an image memory34 for storing image data indicating simulation results and the like; awork memory (internal memory) 36 in which an operation system (OS) isresident; and a display 38 which is a display means. Also, it comprisesan input device 44 which is an input means having a mouse 40 and akeyboard 42 for receiving input data such as the primary condition; aprinter 46 for outputting image data and the like; and a CPU 48 forcontrolling execution of the pesticidal compound indoor behaviorsimulation program 22 and the like.

As the medium drive unit, in conformity to the storage medium 20, aflexible disk unit, CD-ROM drive unit, magnetic tape drive unit, or thelike may be used.

In the following, the processing of the pesticidal compound indoorbehavior simulation program 22 stored in the program area 20 a of thestorage medium 20 will be explained. This processing is performed byexecuting the pesticidal compound indoor behavior simulation program 22read out by the medium drive unit 32. Upon this execution, the mainprogram 22 a of the pesticidal compound indoor behavior simulationprogram 22 is activated.

The subsequent processing operations of the differential equationforming program 22 b, Fugacity calculating program 22 c, indoor behaviorcalculating program 22 d, safety evaluating program 22 e, and minutetime unit changing program 22 f correspond to those explained in theabove-mentioned embodiments and FIGS. 1 and 5.

As explained in the foregoing, the computer program product (storagemedium) employed in each of the above-mentioned embodiments of thepresent invention has a program for initially dividing the environmentinto predetermined media (constituents), simultaneously formingdifferential equations concerning Fugacity of the compound in thesemedium, and then solving them, thereby estimating an indoor behavior ofa compound when a chemical containing the compound is residuallysprayed.

Consequently, the environment is assumed to be a plurality of media, andexchanges of the compound between media and the like are taken intoaccount, whereby simulation results close to the actual behavior of thecompound can be obtained.

The estimation nick time width set when solving the simultaneousdifferential equations is variably set, while constantly confirming massbalance of the compound indoors after the residual spraying, so that theamount of input of the chemical indoors and the resulting solutioncoincide with each other.

Accordingly, since mass balance of the compound after the residualspraying is always monitored such that the amount of input of thecompound indoors and the resulting solution coincide with each other,thereby varying the estimation nick time width; the estimation nick timewidth is set longer when the mass balance fluctuates a little, whereasit is set shorter when the mass balance starts fluctuating greatly.Namely, when solving simultaneous differential equations including aparameter accompanying temporal change, the estimation nick time widthis automatically set in response to the fluctuation in mass balance.Consequently, when processed by a computer, an accurate solution can beobtained in a short time.

Also, the computer program product (storage medium) employed in each ofthe above-mentioned embodiments of the present invention has a programfor evaluating, by use of the above-mentioned estimated results, safetyof a pesticidal compound with respect to the human body when thechemical is residually sprayed.

Accordingly, the safety of the compound with respect to the human bodycan be evaluated accurately in a short time. As a consequence, whenformulating a chemical such as insecticide containing the compound,simulation can be easily repeated while changing conditions, therebymaking it easier to formulate a chemical having a high safety conformingto the aimed object.

Industrial Applicability

In the method of simulating an indoor behavior of a pesticidal compoundin accordance with the present invention, the indoor environment isdivided into predetermined media, and exchanges of the compound betweenmedia and the like are taken into account, whereby simulation resultssimilar to the actual behavior of the compound can be obtained. Also,when solving simultaneous differential equations including a parameteraccompanying a temporal change, a minute time unit can be automaticallyset in response to the fluctuation in mass balance, whereby an accuratesolution can be obtained in a short time when processed by a computer.

The method of simulating an indoor behavior of a pesticidal compound inaccordance with the present invention further comprises a step ofevaluating, according to the indoor behavior of the compound, safety ofthe compound with respect to a human body, whereby the safety of thepesticidal compound can be evaluated accurately in a short time.Accordingly, when formulating a chemical such as insecticide containingthe compound, simulation can be easily repeated while changingconditions, thereby making it easier to formulate a chemical having ahigh safety conforming to the aimed object.

What is claimed is:
 1. A method of simulating an indoor behavior of apesticidal compound, said simulation method comprising: a step ofdividing an indoor environment into predetermined medias; a step ofdetermining under a differential equation, the fugacities with the unitof pressure of said compound in each of said medias, wherein thefugacities are determined in terms selected from emission rate,deposition, V-change, transference, ventilation and degradation; a stepof determining at least one indoor behavior of said compound in theindoor environment from multiplication of fugacity capacity (Z) and saidfugacity (f), and further volume (V) at option in each of said medias,wherein said at least one indoor behavior is selected from a temporalconcentration and residual amount; and a step of monitoring the massbalance of the compound under changing, in response to a fluctuation inthe mass balance of the compound indoors, a minute time unit used whensolving said differential equation.
 2. A simulation method according toclaim 1, further comprising a step of evaluating safety of said compoundwith respect to a human body according to the indoor behavior of saidcompound.
 3. A simulation method according to claim 1, wherein saidcompound-is introduced into an indoor space as a solution containingsaid compound is residually sprayed; and wherein said media are aspraying site, suspended particles which are divided into at least onekind according to size, indoor air, a floor, a wall, and a ceiling.
 4. Asimulation method according to claim 3, wherein said differentialequation at said spraying site is a differential equation stating arelationship among temporal change of fugacity of said compound at saidspraying site, temporal change in volume of said spraying site, amountof attachment of said suspended particles to said spraying site, amountof transference of said compound between said spraying site and anothermedium, and change in amount of degradation of said compound at saidspraying site; wherein said differential equation in said suspendedparticles is a differential equation stating a relationship amongtemporal change of fugacity of said compound in said suspendedparticles, temporal change in volume of said suspended particles, amountof transference of said compound between said suspended particles andanother medium, and change in amount of degradation of said compound insaid suspended particles; wherein said differential equation in saidindoor air is a differential equation stating a relationship amongtemporal change of fugacity of said compound in said indoor air, amountof discharge of said compound outdoors, amount of transference of saidcompound between said indoor air and another medium, and change inamount of degradation of said compound in said indoor air; wherein saiddifferential equation at said floor is a differential equation stating arelationship among temporal change of fugacity of said compound at saidfloor, temporal change in volume of said floor, amount of attachment ofsaid suspended particles to said floor, amount of transference of saidcompound between said floor and another medium, and change in amount ofdegradation of said compound at said floor; wherein said differentialequation at said wall is a differential equation stating a relationshipamong temporal change of fugacity of said compound at said wall,temporal change in volume of said wall, amount of attachment of saidsuspended particles of said wall, amount of transference of the compoundbetween said wall and another medium, and change-in-amount ofdegradation-of said-compound at said wall; and wherein said differentialequation at said ceiling is a differential equation stating arelationship among temporal change of fugacity of said compound at saidceiling, temporal change in volume of said ceiling, amount of attachmentof said suspended particles fo said ceiling, amount of transference ofsaid compound between said ceiling and another medium, and change inamount of degradation of said compound at said ceiling.
 5. A simulationmethod according to claim 1, wherein said compound is introduced into anindoor space as a solution containing said compound is spatiallysprayed; and wherein said media are suspended particles which aredivided into at least one kind according to size, indoor air, a floor, awall, and a ceiling.
 6. A simulation method according to claim 5,wherein said differential equation in said suspended particles is adifferential equation stating a relationship among temporal change offugacity of said compound in said suspended particles, temporal changein volume of said suspended particles, amount of transference of saidcompound between said suspended particles and another medium, and changein amount of degradation of said compound in said suspended particles;wherein said differential equation in said indoor air is a differentialequation stating a relationship among temporal change of fugacity ofsaid compound in said indoor air, amount of discharge of said compoundoutdoors, amount of transference of said compound between said indoorair and another medium, and change in amount of degradation of saidcompound in said indoor air; wherein said difference equation at saidfloor is a differential equation stating a relationship amount temporalchange of fugacity of said compound at said floor, temporal change involume of said floor, amount of attachment of said suspended particlesto said floor, amount of transference of said compound between saidfloor and another medium, and change in amount of degradation of saidcompound at said floor; wherein said differential equation at said wallis a differential equation stating a relationship amount temporal changeof fugacity of said compound at said wall, temporal change in volume ofsaid wall, amount of attachment of said suspended particles to saidwall, amount of transference of said compound between said wall andanother medium, and change in amount of degradation of said compound atsaid wall; and wherein said differential equation at said ceiling is adifferential equation stating a relationship among temporal change offugacity of said compound at said ceiling, temporal change in volume ofsaid ceiling, amount of attachment of said suspended particles of saidceiling, amount of transference of said compound between said ceilingand another medium, and change in amount of degradation of said compoundat said ceiling.
 7. A simulation method according to claim 1, whereinsaid compound is introduced into an indoor space as a solutioncontaining said compound is heated to vaporize; and wherein said mediaare condensed particles which are divided into at least one kindaccording to generation and extinction, high-concentration air,medium-concentration air, low-concentration air, a floor, a wall, and aceiling which is divided into at least one kind according to compoundconcentration.
 8. A simulation method according to claim 7, wherein saiddifferential equation in said condensed particles is a differentialequation stating a relationship among temporal change of fugacity ofsaid compound in said condensed particles, temporal change in volume ofsaid condensed particles, amount of transference of said compoundbetween said condensed particles and another medium, and change inamount of degradation of said compound in said condensed particles;wherein said differential equation in said high-concentration air is adifferential equation stating a relationship among temporal change offugacity of said compound in said high-concentration air, amount ofdischarge of said compound, amount of transference of said compoundbetween said high-concentration air and another medium, and change inamount of degradation of said compound in said high-concentration air;wherein said differential equation in said medium-concentration air isdifferential equation stating a relationship among temporal change offugacity of said compound in said medium-concentration air, amount oftransference of said compound between said medium-concentration air,amount of transference of said compound between saidmedium-concentration air and another medium, and change in amount ofdegradation of said compound in said medium-concentration air; whereinsaid differential equation at said low-concentration air is adifferential equation stating a relationship among temporal change offugacity of said compound in said low-concentration air, amount ofdischarge of said compound outdoors, amount of transference of saidcompound between said low-concentration air and another medium, andchange in amount of degradation of said compound in saidlow-concentration air; wherein said differential equation at said flooris a differential equation stating a relationship among temporal changeof fugacity of said compound at said floor, temporal change in volume ofsaid floor, amount of transference of said compound between said floorand another medium, and change in amount of degradation of said compoundat said floor; wherein said differential equation at said wall is adifferential equation stating a relationship among temporal change offugacity of said compound at said wall, temporal change in volume ofsaid wall, amount of transference of said compound between said wall andanother medium, and change in amount of degradation of said compound atsaid wall; and wherein said difference equation at said ceiling is adifferential equation stating a relationship among temporal change offugacity of said compound at said ceiling, temporal change in volume ofsaid ceiling, amount of transference of said compound between saidceiling and another medium, and change in amount of degradation of saidcompound at said ceiling.
 9. A simulation method according to claim 1,wherein said compound is introduced into an indoor space as a solutioncontaining said compound is sprayed over the whole floor; and whereinsaid medium are suspended particles which are divided into at least onekind according to size, indoor, air, a floor, a wall, and a ceiling. 10.A simulation method according to claim 9, wherein said differentialequation in said suspended particles is a differential equation statinga relationship among temporal change of fugacity of said compound insaid suspended particles, temporal change in volume of said suspendedparticles, amount of transference of said compound between saidsuspended particles and another medium, and change in amount ofdegradation of said compound in said suspended particles; wherein saiddifferential equation in said indoor air is a differential equationstating a relationship among temporal change of fugacity of saidcompound in said indoor air, amount of discharge of said compoundoutdoors, amount of transference of said compound between said indoorair and another medium, and change in amount of degradation of saidcompound in said indoor air; wherein said differential equation at saidfloor is a differential equation stating a relationship among temporalchange of fugacity of said compound at said floor, temporal change involume of said floor, amount of attachment of said suspended particlesto said floor, amount of transference of said compound between saidfloor and another medium, and change in amount of degradation of saidcompound at said floor; wherein said differential equation at said wallis a differential equation stating a relationship among temporal changeof fugacity of said compound at said wall, temporal change in volume ofsaid wall, amount of attachment of said suspended particles to saidwall, amount of transference of said compound between said wall andanother medium, and change in amount of degradation of said compound atsaid wall; and wherein said differential equation of said ceiling is adifferential equation stating a relationship among temporal change offugacity of said compound at said ceiling, temporal change in volume ofsaid ceiling, amount of attachment of said suspended particles of saidceiling, amount of transference of said compound between said ceilingand another medium, and change in amount of degradation of said compoundat said ceiling.
 11. A simulation method according to claim 3, whereinsaid floor is constituted by a rug having ears of fiber; and wherein aspace between said ears is added to said media.
 12. A simulation methodaccording to claim 11, wherein said differential equation in the spacebetween said ears is a differential equation stating a relationshipamong temporal change of fugacity of said compound in the space betweensaid ears, temporal change in volume of the solution containing saidcompound in the space between said ears, amount of attachment of saidcompound into the space portion between said ears by falling, amount oftransference of said compound between the space portion between saidears and another medium, and change in amount of degradation of saidcompound in the space portion between said ears.
 13. A simulation methodaccording to claim 5, wherein said floor is constituted by a rug havingears of fiber; and wherein a space between said ears is added to saidmedia.
 14. A simulation method according to claim 13, wherein saiddifferential equation in the space between said ears is a differentialequation stating a relationship among temporal change of fugacity ofsaid compound in the space between said ears, temporal change in volumeof the solution containing said compound in the space between said ears,amount of attachment of said compound into the space portion betweensaid ears by falling, amount of transference of said compound betweenthe space portion between said ears and another medium, and change inamount of degradation of said compound in the space portion between saidears.
 15. A simulation method according to claim 7, wherein said flooris constituted by a rug having ears of fiber; and wherein a spacebetween said ears is added to said media.
 16. A simulation methodaccording to claim 15, wherein said differential equation in the spacebetween said ears is a differential equation stating a relationshipamong temporal change of fugacity of said compound in the space betweensaid ears, temporal change in volume of the solution containing saidcompound in the space between said ears, amount of attachment of saidcompound into the space portion between said ears by falling, amount oftransference of said compound between the space portion between saidears and another medium, and change in amount of degradation of saidcompound in the space portion between said ears.
 17. A simulation methodaccording to claim 9, wherein said floor is constituted by a rug havingears of fiber; and wherein a space between said ears is added to saidmedia.
 18. A simulation method according to claim 17, wherein saiddifferential equation in the space between said ears is a differentialequation stating a relationship among temporal change of fugacity ofsaid compound in the space between said ears, temporal change in volumeof the solution containing said compound in the space between said ears,amount of attachment of said compound into the space portion betweensaid ears by falling, amount of transference of said compound betweenthe space portion between said ears and another medium, and change inamount of degradation of said compound in the space portion between saidears.
 19. The method according to claim 1, wherein at least one of thefugacities of the compound in each of the medias is determined in termsof V-change, transference and degradation.
 20. The method according toclaim 1, wherein at least one of the fugacities of the compound in eachof the medias is determined in terms of ventilation, transference anddegradation.
 21. The method according to claim 1, wherein at least oneof the fugacities of the compound in each of medias is determined interms of V-change, deposition, transference and degradation.
 22. Themethod according to claim 1, wherein at least one of the fugacities ofthe compound in each of the medias is determined in terms of emissionrate.
 23. A computer product comprising in a program area: a program fordividing an indoor environment into predetermined medias; a program fordetermining under a differential equation, the fugacities with the unitof pressure of said compound in each of said medias, wherein thefugacities are determined in terms selected from emission rate,deposition, V-change, transference, ventilation and degradation; aprogram for determining at least one indoor behavior of said compound inthe indoor environment from multiplication of fugacity capacity (Z) andsaid fugacity (f), and further volume (V) at option in each of saidmedias, wherein said at least one indoor behavior is selected from atemporal concentration and residual amount; and a program for monitoringthe mass balance of the compound under changing, in response to afluctuation in the mass balance of the compound indoor, a minute timeunit used when solving said differential equation.
 24. A computerprogram product according to claim 23, further comprising, in saidprogram area, a program for evaluating safety of said compound withrespect to human-body according to the indoor behavior of said compound.25. A computer program product according to claim 23, wherein saidcompound is introduced into a indoor space as a solution containing saidcompound is residually sprayed; and wherein said media are a sprayingsite, suspended particles which are divided into at least one kindaccording to size, indoor air, a floor, a wall, and a ceiling.
 26. Acomputer program product according to claim 25, wherein saiddifferential equation at said spraying site is a differential equationstating a relationship among temporal change of fugacity of saidcompound in said spraying site, temporal change in volume of saidspraying site, amount of attachment of said suspended particles to saidspraying site, amount of transference of said compound between saidspraying site and another medium, and change in amount of degradation ofsaid compound at said spraying site; wherein said differential equationin said suspended particles is a differential equation stating arelationship among temporal change of fugacity of said suspendedparticles, temporal change in volume of said suspended particles, amountof transference of said compound between said suspended particles andanother medium, and change in amount of degradation of said compound issaid suspended particles; wherein said differential equation in saidindoor air is a differential equation stating a relationship amongtemporal change of fugacity of said compound in said indoor air, amontof discharge of said compound outdoors, amount of transference of saidcompound between said indoor air and another medium, and change inamount of degradation of said compound in said indoor air; wherein saiddifferential equation at said floor is a differential equation stating arelationship among temporal change of fugacity of said compound at saidfloor, temporal change in volume of said floor, amount of attachment ofsaid suspended particles to said floor, amount of transference of saidcompound between said floor and another medium, and change in amount ofdegradation of said compound of said floor; wherein said differentialequation at said wall is a differential equation stating a relationshipamong temporal change of fugacity of said compound at said wall,temporal change in volume of said wall, amount of attachment of saidsuspended particles to said wall, amount of transference of the compoundbetween said wall and another medium, and change in amount ofdegradation of said compound at said wall; and wherein said differentialequation at said ceiling is a differential equation stating arelationship among temporal change of fugacity of said compound at saidceiling, temporal change in volume of said ceiling, amount of attachmentof said suspended particles to said ceiling, amount of transference ofsaid compound between said ceiling and another medium, and change inamount of degradation of said compound at said ceiling.
 27. A computerprogram product according to claim 23, wherein said compound isintroduced into an indoor space as a solution containing said compoundis spatially sprayed; and wherein said media are suspended particleswhich are divided into at least one kind according to size, indoor air,a floor, a wall, and a ceiling.
 28. A computer program product accordingto claim 27, wherein said differential equation in said suspendedparticles is a differential equation stating a relationship amongtemporal change of fugacity of said compound in said suspendedparticles, amount of transference of said compound between saidsuspended particles and another medium, and change in amount ofdegradation of said compound at said suspended particles; wherein saiddifferential equation in said indoor air is a differential equationstating a relationship among temporal change of fugacity of saidcompound in said indoor air, amount of discharge of said compoundoutdoors, amount of transference of said compound between said indoorair and another medium, and change in amount of degradation of saidcompound in said indoor air; wherein said differential equation in saidfloor is a differential equation stating a relationship among temporalchange of fugacity of said compound at said floor, temporal change involume of said floor, amount of attachment of said suspended particlesto said floor, amount of transference of said compound between saidfloor and another medium, and change in amount of degradation of saidcompound at said floor; wherein said differential equation at said wallis a differential equation stating a relationship among temporal changeof fugacity of said compound in said wall, temporal change in volume ofsaid wall, amount of attachment of said suspended particles to saidwall, amount of transference of said compound between said wall andanother medium, and change in amount of degradation of said compound ofsaid wall; and wherein said differential equation at said ceiling is adifferential equation stating a relationship among temporal change offugacity of said compound at said ceiling, temporal change in volume ofsaid ceiling, amount of attachment of said suspended particles to saidceiling, amount of transference of said compound between said ceilingand another medium, and change in amount of degradation of said compoundat said ceiling.
 29. A computer program product according to claim 23,wherein said compound is introduced into an indoor space as a solutioncontaining said compound is heated to vaporize; and wherein said mediaare condensed particles which are divided into at least one kindaccording to generation and extinction, high-concentration air,medium-concentration air, low-concentration air, a floor, a wall, and aceiling which is divided into at least one kind according to compoundconcentration.
 30. A computer program product according to claim 29,wherein said differential equation in said condensed particles in adifferential equation stating a relationship among temporal change offugacity of said compound in said condensed particles, temporal changein volume of said condensed particles, amount of transference of saidcompound between said condensed particles and another medium, and changein amount of degradation of said compound of said condensed particles;wherein said differential equation in said high-concentration air is adifferential equation stating a relationship among temporal change offugacity of said compound in said high-concentration air, amount ofdischarge of said compound, amount of transference of said compoundbetween said high-concentration air and another medium, and change inamount of degradation of said compound in said high-concentration air;wherein said differential equation in said medium-concentration air is adifferential equation stating a relationship among temporal change offugacity of said compound in said medium-concentration air, amount oftransference of said compound between said medium-concentration airandanother medium, and change in amount of degradation of said compoundin said medium-concentration air; wherein said differential equation insaid low-concentration air is a differential equation stating arelationship among temporal change of fugacity of said compound in saidlow-concentration air, amount of discharge of said compound outdoors,amount of transference of said compound between said low-concentrationair and another medium, and change in amount of degradation of saidcompound in said low-concentration air; wherein said differentialequation at said floor is a differential equation stating a relationshipamong temporal change of fugacity of said compound at said floor,temporal change in volume of said floor, amount of transference of saidcompound between said floor and another medium, and change in amount ofdegradation of said compound at said floor; wherein said differentialequation at said wall is a differential equation stating a relationshipamong temporal change of fugacity of said compound at said wall,temporal change in volume of said wall, amount of transference of saidcompound between said wall and another medium, and change in amount ofdegradation of said compound at said wall; and; wherein saiddifferential equation at said ceiling is a differential equation statinga relationship among temporal change of fugacity of said compound atsaid ceiling, temporal change in volume of said ceiling, amount oftransference of said compound between said ceiling and another medium,and change in amount of degradation of said compound at said ceiling.31. A computer program product according to claim 23, wherein saidcompound is introduced into an indoor space as a solution containingsaid compound is sprayed over the whole floor; and wherein said mediaare suspended particles which are divided into at least one kindaccording to size, indoor air, a floor, a wall, and a ceiling.
 32. Acomputer program product according to claim 31, wherein saiddifferential equation in said suspended particles is a differentialequation stating a relationship among temporal change of fugacity ofsaid compound in said suspended particles, temporal change in volume ofsuspended particles, amount of transference of said compound betweensaid suspended particles and another medium, and change in amount ofdegradation of said compound at said suspended particles; wherein saiddifferential equation in said indoor air is a differential equationstating a relationship among temporal change of fugacity of saidcompound in said indoor air, amount of discharge of said compoundoutdoors, amount of transference of said compound between said indoorair and another medium, and change in amount of degradation of saidcompound in said indoor air; wherein said differential equation in saidfloor is a differential equation stating a relationship among temporalchange of fugacity of said compound at said floor, temporal change involume of said floor, amount of attachment of said suspended particlesto said floor, amount of transference of said compound between saidfloor and another medium, and change in amount of degradation of saidcompound at said floor; wherein said differential equation a said wallis a differential equation stating a relationship among temporal changeof fugacity of said compound in said wall, temporal change in volume ofsaid wall, amount of attachment of said suspended particles to saidwall, amount of transference of said compound between said wall andanother medium, and change in amount of degradation of said compound ofsaid wall; and wherein said differential equation at said ceiling is adifferential equation stating a relationship among temporal change offugacity of said compound at said ceiling, temporal change in volume ofsaid ceiling, amount of attachment of said suspended particles to saidceiling, amount of transference of said compound between said ceilingand another medium, and change in amount of degradation of said compoundat said ceiling.
 33. A computer program product according to claim 25,wherein said floor is constituted by a rug having ears of fiber; andwherein a space between said ears is added to said media.
 34. A computerprogram product according to claim 33, wherein a differential equationin the space between said ears is a differential equation stating arelationship among temporal change of fugacity of said compound in thespace between said ears, temporal change in volume of the solutioncontaining said compound in the space between said ears, amount ofattachment of said compound into the space portion between said ears byfalling, amount of transference of said compound between the spaceportion between said ears and another medium, and change in amount ofdegradation of said compound in the space portion between said ears. 35.A computer program product according to claim 27, wherein said floor isconstituted by a rug having ears of fiber; and wherein a space betweensaid ears is added to said media.
 36. A computer program productaccording to claim 35, wherein a differential equation in the spacebetween said ears is a differential equation stating a relationshipamong temporal change of fugacity of said compound in the space betweensaid ears, temporal change in volume of the solution containing saidcompound in the space between said ears, amount of attachment of saidcompound into the space portion between said ears by falling, amount oftransference of said compound between the space portion between saidears and another medium, and change in amount of degradation of saidcompound in the space portion between said ears.
 37. A computer programproduct according to claim 29, wherein said floor is constituted by arug having ears of fiber; and wherein a space between said ears is addedto said media.
 38. A computer program product according to claim 37,wherein said differential equation in the space between said ears is adifferential equation stating a relationship among temporal change offugacity of said compound in the space between said ears, temporalchange in volume of the solution containing said compound in the spacebetween said ears, amount of attachment of said compound into the spaceportion between said ears by falling, amount of transference of saidcompound between the space portion between said ears and another medium,and change in amount of degradation of said compound in the spaceportion between said ears.
 39. A computer program product according toclaim 31, wherein said floor is constituted by a rug having ears offiber; and wherein a space between said ears is added to said media. 40.A computer program product according to claim 39, wherein a differentialequation in the space between said ears is a differential equationstating a relationship among temporal change of fugacity of saidcompound in the space between said ears, temporal change in volume ofthe solution containing said compound in the space between said ears,amount of attachment of said compound into the space portion betweensaid ears by falling, amount of transference of said compound betweenthe space portion between said ears and another medium, and change inamount of degradation of said compound in the space portion between saidears.
 41. A method of simulating an indoor behavior of a pesticidalcompound wherein said compound is introduced into an indoor space as asolution containing said compound, or residually or spatially sprayed,or heated to vaporize, or sprayed over the whole floor, said simulationmethod comprising: a step of dividing an indoor environment intopredetermined medias; a step of determining under a differentialequation, the fugacities with the unit of pressure of said compound ineach of said medias, wherein the fugacities are determined in termsselected from emission rate, deposition, V-change, transference,ventilation and degradation; a step of determining at least one indoorbehavior of said compound in the indoor environment from multiplicationof fugacity capacity (Z) and said fugacity (f), and further volume (V)at option in each of said medias, wherein said at least one indoorbehavior is selected from a temporal concentration and residual amount;and; a step of monitoring the mass balance of the compound underchanging, in response to a fluctuation in the mass balance of thecompound indoor, a minute time unit used when solving said differentialequation.
 42. The simulation method according to claim 41, furthercomprising a step of evaluation safety of said compound with respect toa human body according to the indoor behavior of said compound.